M.Tech Thesis on Simulation and Hardware Implementation of NLMS algorithm on TMS320C6713 Digital Signal Processor

Simulation and Hardware Implementation of NLMS algorithm on
TMS320C6713 Digital Signal Processor
A
Dissertation
submitted
in partial fulfilment
for the award of the Degree of
Master of Technology
in Department of Electronics & Communication Engineering
(with specialization in Digital Communication)

Supervisor

Submitted By:

S.K. Agrawal

Raj Kumar Thenua

Associate Professor

Enrolment No.:
07E2SODCM30P611

Department of Electronics & Communication Engineering
Sobhasaria Engineering College, Sikar
Rajasthan Technical University
April 2011

Candidate’s Declaration
I hereby declare that the work, which is being presented in the Dissertation, entitled
“Simulation

and

Hardware

Implementation

of

NLMS

algorithm

on

TMS320C6713 Digital Signal Processor” in partial fulfilment for the award of
Degree of “Master of Technology” in Deptt. of Electronics & Communication
Engineering with specialization in Digital Communication, and submitted to the
Department

of

Electronics

&

Communication

Engineering,

Sobhasaria

Engineering College Sikar, Rajasthan Technical University is a record of my own
investigations carried under the Guidance of Shri Surendra Kumar Agrawal,
Department of Electronics & Communication Engineering, , Sobhasaria Engineering
College Sikar, Rajasthan.
I have not submitted the matter presented in this Dissertation anywhere for the award
of any other Degree.

(Raj Kumar Thenua)
Digital Communication
Enrolment No.: 07E2SODCM30P611
Sobhasaria Engineering College
Sikar

Counter Signed by
Name(s) of Supervisor(s)

(S.K. Agrawal)

ii

ACKNOWLEDGEMENT
First of all, I would like to express my profound gratitude to my dissertation guide,
Mr. S.K. Agrawal (Head of the Department), for his outstanding guidance and
support during my dissertation work. I benefited greatly from working under his
guidance. His encouragement, motivation and support have been invaluable
throughout my studies at Sobhasaria Engineering College, Sikar.
I would like to thank Mohd. Sabir Khan (M.Tech coordinator) for his excellent
guidance and kind co-operation during the entire study at Sobhasaria Engineering
College, Sikar.
I would also like to thank all the faculty members of ECE department who have
co-operated and encouraged during the study course.
I would also like to thank all the staff (technical and non-technical) and librarians of
Sobhasaria Engineering College, Sikar who have directly or indirectly helped during
the course of my study.
Finally, I would like to thank my family & friends for their constant love and support
and for providing me with the opportunity and the encouragement to pursue my goals.

Raj Kumar Thenua

iii

CONTENTS

Candidate’s Declaration

ii

Acknowledgement

iii

Contents

iv-vi

List of Tables

vii

List of Figures

viii-x

List of Abbreviations

xi-xii

List of Symbols

xiii

ABSTRACT

1

CHAPTER 1: INTRODUCTION

2

1.1

Overview

2

1.2

Motivation

3

1.3

Scope of the work

4

1.4

Objectives of the thesis

5

1.5

Organization of the thesis

5

CHAPTER 2: LITERATURE SURVEY

7

CHAPTER 3: ADAPTIVE FILTERS

12

3.1

Introduction

12

3.1.1 Adaptive Filter Configuration

13

3.1.2 Adaptive Noise Canceller (ANC)

16

Approaches to Adaptive filtering Algorithms

19

3.2.1 Least Mean Square (LMS) Algorithm

20

3.2

3.2.1.1 Derivation of the LMS Algorithm

20

3.2.1.2 Implementation of the LMS Algorithm

21

3.2.2 Normalized Least Mean Square (NLMS) Algorithm

22

3.2.2.1 Derivation of the NLMS Algorithm

23

3.2.2.2 Implementation of the NLMS Algorithm

24

3.2.3 Recursive Least Square (RLS) Algorithm

iv

24

3.2.3.1 Derivation of the RLS Algorithm
3.2.3.2 Implementation of the RLS Algorithm
3.3

25
27

Adaptive filtering using MATLAB

28

CHAPTER 4: SIMULINK MODEL DESIGN FOR HARDWARE
IMPLEMENTATION

31

4.1

Introduction to Simulink

31

4.2

Model design

32

4.2.1 Common Blocks used in Building Model

32

4.2.1.1 C6713 DSK ADC Block

32

4.2.1.2 C6713 DSK DAC Block

33

4.2.1.3 C6713 DSK Target Preferences Block

33

4.2.1.4 C6713 DSK Reset Block

33

4.2.1.5 NLMS Filter Block

34

4.2.1.6 C6713 DSK LED Block

34

4.2.1.7 C6713 DSK DIP Switch Block

34

4.2.2 Building the model
Model Reconfiguration

37

4.3.1 The ADC Setting

38

4.3.2 The DAC Settings

39

4.3.3 Setting the NLMS Filter Parameters

40

4.3.4 Setting the Delay Parameters

41

4.3.5 DIP Switch Settings

41

4.3.6 Setting the Constant Value

42

4.3.7 Setting the Constant Data Type

43

4.3.8 Setting the Relational Operator Type

43

4.3.9 Setting the Relational Operator Data Type

43

4.3.10 Switch Setting

4.3

34

44

CHAPTER 5: REAL TIME IMPLEMENTATION ON DSP PROCESSOR 45
5.1

Introduction to Digital Signal Processor (TMS320C6713)

45

5.1.1 Central Processing Unit Architecture

48

5.1.2 General purpose registers overview

49

v

5.1.3 Interrupts

49

5.1.4 Audio Interface Codec

50

5.1.5 DSP/BIOS & RTDX

52

5.2

Code Composer Studio as Integrated Development Environment

54

5.3

MATLAB interfacing with CCS and DSP Processor

58

5.4

Real-time experimental Setup using DSP Processor

58

CHAPTER 6: RESULTS AND DISCUSSION

63

6.1

MATLAB simulation results for Adaptive Algorithms

63

6.1.1

LMS Algorithm Simulation Results

64

6.1.2

NLMS Algorithm Simulation Results

66

6.1.3

RLS Algorithm Simulation Results

67

6.1.4

Performance Comparison of Adaptive Algorithms

67

6.2

Hardware Implementation Results using TMS320C6713 Processor

71

6.2.1 Tone Signal Analysis using NLMS Algorithm

71

6.2.1.1 Effect on Filter Performance at Various Frequencies

73

6.2.1.2 Effect on Filter Performance at Various Amplitudes

75

6.2.2 ECG Signal Analysis using NLMS and LMS Algorithms and their

78

Performance Comparison
CHAPTER 7: CONCLUSIONS

85

7.1

Conclusion

85

7.2

Future Work

86

REFERENCES

88

APPENDIX-I

LIST OF PUBLICATIONS

93

APPENDIX-II

MATLAB COMMANDS

94

vi

LIST OF TABLES
Table No.

Title

Page No.

Table 6.1

Mean Squared Error (MSE) Versus Step Size (µ)

65

Table 6.2

Mean Squared Error versus Filter-order (N)

69

Table 6.3

Performance comparison of various adaptive algorithms

70

Table 6.4

Comparison of Various Parameters for Adaptive Algorithms

70

Table 6.5

SNR Improvement versus voltage and frequency

78

Table 6.6

SNR Improvement versus noise level for a Tone Signal

78

Table 6.7

SNR Improvement versus noise variance for an ECG Signal

84

vii

LIST OF FIGURES
Figure No.

Title

Page No.

Fig.3.1

General adaptive filter configuration

14

Fig.3.2

Transversal FIR filter architecture

15

Fig.3.3

Block diagram for Adaptive Noise Canceller

16

Fig.3.4

MATLAB versatility diagram

29

Fig.4.1

Simulink applications

32

Fig.4.2

Adaptive Noise cancellation Simulink model

33

Fig.4.3

Simulink library browser

35

Fig.4.4

Blank new model window

36

Fig.4.5

Model window with ADC block

37

Fig.4.6

Model illustration before connections

38

Fig.4.7

Setting up the ADC for mono microphone input

39

Fig.4.8

Setting the DAC parameters

39

Fig.4.9

Setting the NLMS filter parameters

40

Fig.4.10

Setting the delay unit

41

Fig.4.11

Setting up the DIP switch values

42

Fig.4.12

Setting the constant parameters

42

Fig.4.13

Data type conversion to 16-bit integer

43

Fig.4.14

Changing the output data type

44

Fig.5.1

Block diagram of TMS320C6713 processor

47

Fig.5.2

Physical overview of the TMS320C6713 processor

47

Fig.5.3

Functional block diagram of TMS320C6713 CPU

48

Fig.5.4

Interrupt priority diagram

49

Fig.5.5

Interrupt handling procedure

50

viii

Figure No.

Title

Page No.

Fig.5.6

Audio connection illustrating control and data signal

51

Fig.5.7

AIC23 codec interface

52

Fig.5.8

DSP BIOS and RTDX

53

Fig.5.9

Code composer studio platform

54

Fig.5.10

Embedded software development

54

Fig.5.11

Typical 67xx efficiency vs. efforts level for different codes

55

Fig.5.12

Code generation

55

Fig.5.13

Cross development environment

56

Fig.5.14

Signal flow during processing

56

Fig.5.15

Real-time analysis and data visualization

57

Fig.5.16

MATLAB interfacing with CCS and TI target processor

58

Fig.5.17

Experimental setup using Texas Instrument processor

59

Fig.5.18

Real-time setup using Texas Instrument processor

59

Fig.5.19

Model building using RTW

60

Fig.5.20

Code generation using RTDX link

60

Fig.5.21

Target processor in running status

61

Fig.5.22 (a) Switch at Position 0

62

Fig.5.22 (b) Switch at position 1 for NLMS noise reduction

62

Fig.6.1(a)

Clean tone(sinusoidal) signal s(n)

63

Fig.6.1(b)

Noise signal x(n)

63

Fig.6.1(c)

Delayed noise signal x1(n)

64

Fig.6.1(d)

Desired signal d(n)

64

Fig.6.2

MATLAB simulation for LMS algorithm; N=19, step size=0.001

64

Fig.6.3

MATLAB simulation for NLMS algorithm; N=19, step size=0.001

66

ix

Figure No.

Title

Page No.

Fig.6.4

MATLAB simulation for RLS algorithm; N=19, λ =1

67

Fig.6.5

MSE versus step-size (µ) for LMS algorithm

67

Fig.6.6

MSE versus filter order (N)

68

Fig.6.7

Clean tone signal of 1 kHz

72

Fig.6.8

Noise corrupted tone signal

72

Fig.6.9

Filtered tone signal

73

Fig.6.10

Time delay in filtered signal

73

Fig.6.11(a)

Filtered output signal at 2 kHz frequency

74

Fig.6.11(b)


74

Fig.6.11(c)


75

Fig.6.11(d)


75

Fig.6.12(a)

Filtered output signal at 3V

76

Fig.6.12(b)


76

Fig.6.12(c)


77

Fig.6.13

Filtered signal at high noise

77

Fig.6.14

ECG waveform

79

Fig.6.15

Clean ECG signal

80

Fig.6.16(a)

NLMS filtered output for low level noisy ECG signal

81

Fig.6.16(b)

LMS filtered output for low level noisy ECG signal

81

Fig.6.17(a)

NLMS filtered output for medium level noisy ECG signal

82

Fig.6.17(b)

LMS filtered output for medium level noisy ECG signal

82

Fig.6.18(a)

NLMS filtered output for high level noisy ECG signal

83

Fig.6.18(b)

LMS filtered output for high level noisy ECG signal

83

x

LIST OF ABBREBIATIONS
ANC

Adaptive Noise Cancellation

API

Application Program Interface

AWGN

Additive White Gaussian Noise

BSL

Board Support Library

BIOS

Basic Input Output System

CSL

Chip Support Library

CCS

Code Composer Studio

CODEC

Coder Decoder

COFF

Common Object File Format

COM

Component Object Model

CPLD

Complex Programmable Logic Device

CSV

Comma Separated Value

DIP

Dual Inline Package

DSK

Digital signal processor Starter Kit

DSO

Digital Storage Oscilloscope

DSP

Digital Signal Processor

ECG

Electrocardiogram

EDMA

Enhanced Direct Memory Access

EMIF

External Memory Interface

FIR

Finite Impulse Response

FPGA

Field Programmable Gate Array

FTRLS

Fast Transversal Recursive Least Square

GEL

General Extension Language

GPIO

General Purpose Input Output

GUI

Graphical User Interface

HPI

Host Port Interface

IDE

Integrated Development Environment

IIR

Infinite Impulse Response

JTAG

Joint Text Action Group

LMS

Least Mean Square

xi

LSE

Least Square Error

MA

Moving Average

McBSP

Multichannel Buffered Serial Port

McASP

Multichannel Audio Serial Port

MSE

Mean Square Error

MMSE

Minimum Mean Square Error

NLMS

Normalized Least Mean Square

RLS

Recursive Least Squares

RTDX

Real Time Data Exchange

RTW

Real Time Workshop

SNR

Signal to Noise Ratio

TI

Texas Instrument

TVLMS

Time Varying Least Mean Squared

VLIW

Very Long Instruction Word

VSLMS

Variable Step-size Least Mean Square

VSSNLMS

Variable Step Size Normalized Least Mean Square

xii

LIST OF SYMBOLS
s(n)

Source signal

x(n)

Noise signal or reference signal

x1(n)

Delayed noise signal

w(n)

Filter weights

d(n)

Desired signal

y(n)

FIR filter output

e(n)

Error signal

+

e (n)

Advance samples of error signal

e (n)

Error estimation

n

Sample number

i

Iteration

N

Filter order

E

Ensemble

Z-1

Unit delay

wT

Transpose of weight vector

µ

Step size
Gradient

ξ

Cost function
x(n)

2

Squared Euclidian norm of the input vector x(n) at iteration n.

c

Constant term for normalization

α

NLMS adaption constant

λ
~
Λ ( n)

Small positive constant

k(n)
~
ψ ( n)

Gain vector

λ

~

Diagonal matrix vector

Intermediate matrix

θλ

Intermediate vector

w ( n)

Estimation of filter weight vector

y ( n)

Estimation of FIR filter output

xiii

ABSTRACT
Adaptive filtering constitutes one of the core technology in the field of digital signal
processing and finds numerous application in the areas of science and technology viz. echo
cancellation, channel equalization, adaptive noise cancellation, adaptive beam-forming,
biomedical signal processing etc.
Noise problems in the environment have gained attention due to the tremendous growth in
upcoming technologies which gives spurious outcomes like noisy engines, heavy machinery,
high electromagnetic radiation devices and other noise sources. Therefore, the problem of
controlling the noise level in the area of signal processing has become the focus of a vast
amount of research over the years.
In this particular work an attempt has been made to explore the adaptive filtering techniques
for noise cancellation using Least Mean Square (LMS), Normalized Least Mean Square
(NLMS) and Recursive Least Mean Square (RLS) algorithms. The mentioned algorithms
have been simulated in MATLAB and compared for evaluating the best performance in terms
of Mean Squared Error (MSE), convergence rate, percentage noise removal, computational
complexity and stability.
In the specific example of tone signal, LMS has shown low convergence rate, with low
computational complexity while RLS has fast convergence rate and shows best performance
but at the cost of large computational complexity and memory requirement. However the
NLMS provides a trade-off in convergence rate and computational complexity which makes
it more suitable for hardware implementation.
The hardware implementation of NLMS algorithm is performed for that a simulink model is
designed to generate auto C code for the DSP processor. The generated C code is loaded on
the DSP processor hardware and the task of real-time noise cancellation is done for the two
types of signals i.e. tone signal and biomedical ECG signal. For both types of signals, three
noisy signals of different noise levels are used to judge the performance of the designed
system. The output results are analysed using Digital Storage Oscilloscope (DSO) in terms of
filtered signal SNR improvement. The results have also been compared with the LMS
algorithm to prove the superiority of NLMS algorithm.

1

Chapter-1

INTRODUCTION
In the process of transmission of information from the source to receiver, noise from
the surroundings automatically gets added to the signal. The noisy signal contains two
components, one carries the information of interest i.e. the useful signal; the other consists of
random errors or noise which is superimposed on the useful signal. These random errors or
noise are unwanted because they diminish the accuracy and precision of the measured signal.
Therefore the effective removal or reduction of noise in the field of signal processing is an
active area of research.

1.1

Overview
The use of adaptive filter [1] is one of the most popular proposed solutions to reduce

the signal corruption caused by predictable and unpredictable noise. An adaptive filter has
the property of self-modifying its frequency response to change its behavior with time. It
allows the filter to adapt to the response as the input signal characteristics change. Due to this
capability and the construction flexibility, the adaptive filters have been employed in many
different applications like telephonic echo cancellation, radar signal processing, navigation
systems, communications, channel equalization, bio-medical & biometric signal processing
etc.
In the field of adaptive filtering, there are mainly two algorithms that are used to force
the filter to adapt its coefficients – Stochastic gradient based algorithm and Recursive Least
Square based algorithm. Their implementations and adaptation properties are the determining
factors for choice of application. The main requirements and the performance parameters for
adaptive filters are the convergence speed and the asymptotic error. The convergence speed is
the primary property of an adaptive filter which enables one to measure how quickly the filter
is converging to the desired value. It is a major requirement as well as a limiting factor for
most of the applications of adaptive filters.
The asymptotic error represents the amount of error that the filter introduces at steady
state after it has converged to the desired value. The RLS filters due to their computational
structure have considerably better properties than the LMS filters both in terms of the

2

convergence speed and the asymptotic error. The RLS filters which outperform the LMS
filters obtain their solution for the weight updated directly from the Mean Square Error
(MSE) [2]. However, they are computationally very demanding and also very dependent
upon the precision of the input signal. Their computational requirements are significant and
imply the use of expensive and power demanding high-speed processors. Also, for the
systems lacking the appropriate dynamic range, the adaptation algorithms can become
unstable. In this manner to match the computational requirements a DSP processor can be a
better substitute.

1.2

Motivation
In the field of signal processing there is a significant need of a special class of digital

filters known as adaptive filters. Adaptive filters are used commonly in many different
configurations for different applications. These filters have various advantages over the
standard digital filters. They can adapt their filter coefficients from the environment
according to preset rules. The filters are capable of learning from the statistics of current
conditions and change their coefficients in order to achieve a certain goal. In order to design a
filter prior knowledge of the desired response is required. When such knowledge is not
available due to the changing nature of the filter’s requirements, it is impossible to design a
standard digital filter. In such situations, adaptive filters are desirable.
The algorithms used to perform the adaptation and the configuration of the filter
depends directly on the application of the filter. However, the basic computational engine that
performs the adaptation of the filter coefficients can be the same for different algorithms and
it is based on the statistics of the input signals to the system. The two classes of adaptive
filtering algorithms namely Recursive Least Squares (RLS) and Least Mean Squared (LMS)
are capable of performing the adaptation of the filter coefficients.
When we talk about a real scenario where the information generated from the source
side gets contaminated by the noise signal, this situation demands for the adaptive filtering
algorithm which provides fast convergence while being numerically stable without
incorporating much memory.

3

Hence, the motivation for the thesis is to search for an adaptive algorithm which has
reduced computational complexity, reasonable convergence speed and good stability without
degrading the performance of the adaptive filter and then realize the algorithm on an efficient
hardware which makes it more practical in real time applications.

1.3

Scope of the Work
In numerous application areas, including biomedical engineering, radar & sonar

engineering, digital communications etc., the goal is to extract the useful signal corrupted by
interferences and noises. In this wok an adaptive noise canceller will be designed that will
more effective than available ones. To achieve an effective adaptive noise canceller, the
simulation of various adaptive algorithms will be done on MATLAB. The obtained suitable
algorithm will be implemented on the TMS320C6713 DSK hardware. The designed system
will be tested for the filtering of a noisy ECG signal and tone signal and the system
performance will be compared with the early designed available systems. The designed
system may be useful for cancelling of interference in ECG signal, periodic interference in
audio signal and broad-band interference in the side-lobes of an antenna array.
In this work for the simulation, MATLAB version 7.4.0.287(R2007a) is used, though
Labview version7 may also be applicable. For the hardware implementation, Texas
Instrument (TI) TMS320C6713 digital signal processor is used. However, Field
Programmable Gate Array (FPGA) may also be suitable. To assist the hardware
implementation Simulink version 6.6 is appropriate to generate C code for the DSP hardware.
To communicate with DSP processor, Integrated Development Environment (IDE) software
Code Composer Studio V3.1 is essential. Function generator and noise generator or any other
audio device can be used as an input source for signal analysis. For the analysis of output data
DSO is essentially required however CRO may also be used.
Current adaptive noise cancellation models [5], [9], [11] works on relatively low
processing speed that is not suitable for real-time signals which results delay in output. In this
direction, to increase the processing speed and to improve signal-to-noise ratio, a DSP
processor can be useful because it is a fast special purpose microprocessor with a specialized
type of architecture and an appropriate instruction set for signal processing. It is also well
suited for numerically intensive calculations.

4

1.4

Objectives of the Thesis
The core of this thesis is to analyze and filter the noisy signals (real-time as well as

non-real time) by various adaptive filtering techniques in software as well as in hardware,
using MATLAB & DSP processor respectively.
The basic objective is to focus on the hardware implementation of adaptive algorithms
for filtering so the DSP processor is employed in this work as it can deal more efficiently
with real-time as well as non-real time signals.
The objectives of the thesis are as follows:
(a) To perform the MATLAB simulation of Least Mean Squared (LMS), Normalized
Least Mean Squared (NLMS) and Recursive Least Square (RLS) algorithms and to
compare their relative performance with a tone signal.
(b) Design a simulink model to generate auto C code for the hardware implementation
of NLMS and LMS algorithms.
(c) Hardware implementation of NLMS and LMS algorithms to perform the analysis
of an ECG signal and tone signal.
(d) To compare the performance of NLMS and LMS algorithms in terms of SNR
improvement for an ECG signal.

1.5

Organization of the Thesis
The work emphasizing on the implementation of various adaptive filtering algorithms

using MATLAB, Simulink and DSP processor, in this regard the thesis is divided into seven
chapters as follows:
Chapter-2 deals with the literature survey for the presented work, where so many
papers from IEEE and other refereed journals or proceedings are taken which relate the
present work with recent research work going on worldwide and assure the consistency of the
work.
Chapter-3 presents a detailed introduction of adaptive filter theory and various
adaptive filtering algorithms with problem definition.

5

Chapter-4 presents a brief introduction of simulink. An adaptive noise cancellation
model is designed for adaptive noise cancellation with the capability of C code generation to
implement on DSP processor.
Chapter-5 illustrates experimental setup for the real-time implementation of an
adaptive noise canceller on a DSK. Therefore a brief introduction of TMS320C6713
processor and code composer studio (CCS) with real-time workshop facility is also presented.
Chapter-6 shows the experimental outcomes for the various algorithms. This chapter
is divided in two parts, first part shows the MATLAB simulation results for a sinusoidal tone
signal and the second part illustrates the real time DSP Processor implementation results for
sinusoidal tone signal and ECG signal. The results from DSP processor are analyzed with the
help of DSO.
Chapter-7 summarizes the work and provides suggestions for future research.

6

Chapter-2

LITERATURE SURVEY
In the last thirty years significant contributions have been made in the field of signal
processing. The advances in digital circuit design have been the key technological
development that sparked a growing interest in the field of digital signal processing. The
resulting digital signal processing systems are attractive due to their low cost, reliability,
accuracy, small physical sizes and flexibility.
In numerous applications of signal processing, communications and biomedical we
face the necessity to remove noise and distortion from the signals. These phenomena are due
to time-varying physical processes which are unknown sometimes. One of these situations is
during the transmission of a signal from one point to another. The channel which may be of
wires, fibers, microwave beam etc., introduces noise and distortion due to the variations of its
properties. These variations may be slow or fast. Since most of the time the variations are
unknown, so there is a requirement of such type of filters that can work effectively in such
unknown environment. The adaptive filter is the right choice that diminishes and sometimes
completely eliminates the signal distortion.
The most common adaptive filters which are used during the adaption process are the
finite impulse response (FIR) types. These are preferable because they are stable, and no
special adjustments are needed for their implementation. In adaptive filters, the filter weights
are needed to be updated continuously according to certain rules. These rules are presented in
form of algorithms. There are mainly two types of algorithms that are used for adaptive
filtering. The first is stochastic gradient based algorithm known as Least Mean Squared
(LMS) algorithm and second is based on least square estimation which is known as Recursive
Least Square (RLS) algorithm. A great deal of research [1]-[5], [14], [15] has been carried
out in subsequent years for finding new variant of these algorithms to achieve better
performance in noise cancellation applications.
Bernard Widrow et. al.[1] in 1975, described the adaptive noise cancelling as an
alternative method of estimating signals which are corrupted by additive noise or interference
by employing LMS algorithm. The method uses a “primary” input containing the corrupted
signal and a “reference” input containing noise correlated in some unknown way with the

7

primary noise. The reference input is adaptively filtered and subtracted from the primary
input to obtain the signal estimate. Widrow [1] focused on the usefulness of the adaptive
noise cancellation technique in a variety of practical applications that included the cancelling
of various forms of periodic interference in electrocardiography, the cancelling of periodic
interference in speech signals, and the cancelling of broad-band interference in the side-lobes
of an antenna array.
In 1988, Ahmed S. Abutaleb [2] introduced a new principle- Pontryagin minimum
principal to reduce the computational time of LMS algorithm. The proposed method reduces
the computation time drastically without degrading the accuracy of the system. When
compared to the LMS-based widrow [1] model, it was shown to have superior performance.
The LMS based algorithms are simple and easy to implement but the convergence speed is
slow. Abhishek Tandon et. al.[3] introduced an efficient, low-complexity Normalized least
mean squared (NLMS) algorithm for echo cancellation in multiple audio channels. The
performance of the proposed algorithm was compared with other adaptive algorithms for
acoustic echo cancellation. It was shown that the proposed algorithm has reduced complexity,
while providing a good overall performance.
In NLMS algorithm, all the filter coefficients are updated for each input sample. Dong
Hang et. al.[4] presented a multi-rate algorithm which can dynamically change the update
rate of the coefficients of filter by analyzing the actual application environment. When the
environment is varying, the rate increases while it decreases when the environment is stable.
The results of noise cancellation indicate that the new method has faster convergence speed,
low computation complexity, and the same minimum error as the traditional method.
Ying He et. al.[5] presented the MATLAB simulation of RLS algorithm and the
performance was compared with LMS algorithm. The convergence speed of RLS algorithm
is much faster and produces a minimum mean squared error (MSE) among all available LMS
based algorithms but at the cost of increased computational complexity which makes its
implementation difficult on hardware.
Nowadays the availability of high speed digital signal processors has attracted the
attention of the research scholars towards the real-time implementation of the available
algorithms on the hardware platform. Digital signal processors are fast special-purpose

8

microprocessors with a specialized type of architecture and an instruction set appropriate for
signal processing. The architecture of the digital signal processor is very well suited for
numerically intensive calculations. DSP techniques have been very successful because of the
development of low-cost software and hardware support. DSP processors are concerned
primarily with real-time signal processing.

DSP processors exploit the advantages of

microprocessors. They are easy to use, flexible, economical and can be reprogrammed easily.
The starting of real-time hardware implementation was done by Edgar Andrei [6]
initially on the Motorola DSP56307 in 2000. Later in year 2002, Michail D. Galanis et. al.[7]
presented a DSP course for real-time systems design and implementation based on the
TMS320C6211. This course emphasized the issue of transition from an advanced design and
simulation environment like MATLAB to a DSP software environment like Code Composer
Studio.
Boo-Shik Ryu et. al.[8] implemented and investigated the performance of a noise
canceller with DSP processor (TMS320C6713) using the LMS algorithm, NLMS algorithm
and VSS-NLMS algorithm. Results showed that the proposed combination of hardware and
VSS-NLMS algorithm has not only a faster convergence rate but also lower distortion when
compared with the fixed step size LMS algorithm and NLMS algorithm in real time
environments.
In 2009, J. Gerardo Avalos et. al. [9] have done an implementation of a digital
adaptive filter on the digital signal processor TMS320C6713 using a variant of the LMS
algorithm which consists of error codification. The speed of convergence is increased and the
complexity of design for its implementation in digital adaptive filters is reduced because the
resulting codified error is composed of integer values. The LMS algorithm with codified error
(ECLMS) was tested in an environmental noise canceller and the results demonstrate an
increase in the convergence speed and a reduction of processing time.
C.A. Duran et. al. [10] presented an implementation of the LMS, NLMS and other
LMS based algorithms on the DSK TMS320C6713 with the intention to compare their
performance, analyze their time & frequency behavior along with the processing speed of the
algorithms. The objective of the NLMS algorithm is to obtain the best convergence factor
considering the input signal power in order to improve the filter convergence time. The

9

obtained results show that the NLMS has better performance than the LMS. Unfortunately,
the computational complexity increases which means more processing time.
The work related to real-time implementation so far discussed was implemented on
DSP processor by writing either assembly or C program directly in the editor of Code
Composer Studio (CCS). The writing of assembly program needs so many efforts therefore
only professional person can do this similarly C programming are not simple as far as
hardware implementation concerned.
There is a simple way to create C code automatically which requires less effort and is
more efficient. Presently only few researchers [11]-[13] are aware about this facility which is
provided by the MATLAB Version 7.1 and higher versions, using embedded target Real-time
Workshop (RTW). Gaurav Saxena et. al. [11] have used this auto code generation facility
and presented better results than the conventional C code writing.
Gaurav Saxena et. al. [11] discussed the real time implementation of adaptive noise
cancellation based on an improved adaptive wiener filter on Texas Instruments
TMS320C6713 DSK. Then its performance was compared with the Lee’s adaptive wiener
filter. Furthermore, a model based design of adaptive noise cancellation based on LMS filter
using simulink was implemented on TI C6713. The auto-code generated by the Real Time
Workshop for the simulink model of LMS filter was compared with the ‘C’ implementation
of LMS filter on C6713 in terms of code length and computation time. It was found to have a
large improvement in computation time but at the cost of increased code length.
S.K. Daruwalla et. al. [12] focused on the development and the real time
implementation of various audio effects using simulink blocks by employing an audio signal
as input. This system has helped the sound engineers to easily configure/capture various
audio effects in advance by simply varying the values of predefined simulink blocks. The
digital signal processor is used to implement the designs; this broadens the versatility of
system by allowing the user to employ the processor for any audio input in real-time. The
work is enriched with the real-time concepts of controlling the various audio effects via onboard DIP switches on the C6713 DSK.

10

In Nov-2009, Yaghoub Mollaei [13] designed an adaptive FIR filter with normalized
LMS algorithm to cancel the noise. A simulink model is created and linked to TMS320C6711
digital signal processor through embedded target for C6000 SIMULINK toolbox and realtime workshop to perform hardware adaptive noise cancellation. Three noises with different
powers were used to test and judge the system performance in software and hardware. The
background noises for speech and music track were eliminated adequately with reasonable
rate for all the tested noises.
The outcomes of the literature survey can be summarized as follows:
The adaptive filters are attractive to work in an unknown environment and are suitable
for noise cancellation applications in the field of digital signal processing.
To update the adaptive filter weights two types of algorithms, LMS & RLS are used.
RLS based algorithms have better performance but at the cost of larger computational
complexity therefore very less work [5], [15] is going on in this direction. On the
other hand, LMS based algorithms are simple to implement and its few variants like
NLMS have comparable performance with RLS algorithm. So a large amount of
research [1]-[5] through simulation has been carried out in this regard to improve the
performance of LMS based algorithms.
Simulation can be carried out on non-real time signals only. Therefore for real-time
application there is a need of the hardware implementation of LMS based algorithms.
The DSP processor has been found to be a suitable hardware for signal processing
applications.
Hence, there is a requirement to find out the easiest way for the hardware
implementation of adaptive filter algorithms on a particular DSP processor. The use
of simulink model [11]-[13] with embedded target and real time workshop has proved
to be helpful for the same.
Therefore the simulink based hardware implementation of NLMS algorithm for ECG
signal analysis can be a good contribution in the field of adaptive filtering.

11

Chapter-3

ADAPTIVE FILTERS
3.1

Introduction
Filtering is a signal processing operation. Its objective is to process a signal in order to

manipulate the information contained in the signal. In other words, a filter is a device that
maps its input signal to another output signal facilitating the extraction of the desired
information contained in the input signal. A digital filter is the one that processes discretetime signals represented in digital format. For time-invariant filters the internal parameters
and the structure of the filter are fixed, and if the filter is linear the output signal is a linear
function of the input signal. Once the prescribed specifications are given, the design of timeinvariant linear filters entails three basic steps namely; the approximation of the
specifications by a rational transfer function, the choice of an appropriate structure defining
the algorithm, and the choice of the form of implementation for the algorithm.
An adaptive filter [1], [2] is required when either the fixed specifications are unknown
or the specifications cannot be satisfied by time-invariant filters. Strictly speaking, an
adaptive filter is a nonlinear filter since its characteristics are dependent on the input signal
and consequently the homogeneity and additivity conditions are not satisfied. However, if we
freeze the filter parameters at a given instant of time, most adaptive filters are linear in the
sense that their output signals are linear functions of their input signals.
The adaptive filters are time-varying since their parameters are continuously changing
in order to meet a performance requirement. In this sense, we can interpret an adaptive filter
as a filter that performs the approximation step on-line. Usually, the definition of the
performance criterion requires the existence of a reference signal that is usually hidden in the
approximation step of fixed-filter design.
Adaptive filters are considered nonlinear systems; therefore their behaviour analysis is
more complicated than for fixed filters. On the other hand, since the adaptive filters are self
designing filters from the practitioner’s point of view, their design can be considered less
involved than the digital filters with fixed coefficients.

12

Adaptive filters work on the principle of minimizing the mean squared difference
(or error) between the filter output and a target (or desired) signal. Adaptive filters are used
for estimation of non-stationary signals and systems, or in applications where a sample-by
sample adaptation of a process and a low processing delay is required.
Adaptive filters are used in applications [26]-[29] that involve a combination of three
broad signal processing problems:
(1) De-noising and channel equalization – filtering a time-varying noisy signal to remove the
effect of noise and channel distortions.
(2) Trajectory estimation – tracking and prediction of the trajectory of a non stationary signal
or parameter observed in noise.
(3) System identification – adaptive estimation of the parameters of a time-varying system
from a related observation.
Adaptive linear filters work on the principle that the desired signal or parameters can
be extracted from the input through a filtering or estimation operation. The adaptation of the
filter parameters is based on minimizing the mean squared error between the filter output and
a target (or desired) signal. The use of the Least Square Estimation (LSE) criterion is
equivalent to the principal of orthogonality in which at any discrete time m the estimator is
expected to use all the available information such that any estimation error at time m is
orthogonal to all the information available up to time m.

3.1.1 Adaptive Filter Configuration
The general set up of an adaptive-filtering environment is illustrated in Fig.3.1 [43],
where n is the iteration number, x(n) denotes the input signal, y(n) is the adaptive-filter output
signal, and d(n) defines the desired signal. The error signal e (n) is calculated as d (n) – y (n).
The error signal is then used to form a performance function that is required by the adaptation
algorithm in order to determine the appropriate updating of the filter coefficients. The
minimization of the objective function implies that the adaptive-filter output signal is
matching the desired signal in some sense. At each sampling time, an adaptation algorithm
adjusts the filter coefficients w(n) =[w0(n)w1(n)….. wN−1(n)] to minimize the difference
between the filter output and a desired or target signal.

13

d(n)

y(n)

Adaptive
Filter

x(n)

_

⊕
e(n)

Adaptive
Algorithm

Fig.3.1. General Adaptive filter configuration

The complete specification of an adaptive system, as shown in Fig. 3.1, consists of
three things:
(a) Input: The type of application is defined by the choice of the signals acquired
from the environment to be the input and desired-output signals. The number of different
applications in which adaptive techniques are being successfully used has increased
enormously during the last two decades. Some examples are echo cancellation, equalization
of dispersive channels, system identification, signal enhancement, adaptive beam-forming,
noise cancelling and control.
(b) Adaptive-filter structure: The adaptive filter can be implemented in a number of
different structures or realizations. The choice of the structure can influence the
computational complexity (amount of arithmetic operations per iteration) of the process and
also the necessary number of iterations to achieve a desired performance level. Basically,
there are two major classes of adaptive digital filter realization, distinguished by the form of
the impulse response, namely the finite-duration impulse response (FIR) filter and the
infinite-duration impulse response (IIR) filters. FIR filters are usually implemented with nonrecursive structures, whereas IIR filters utilize recursive realizations.
Adaptive FIR filter realizations: The most widely used adaptive FIR filter structure
is the transversal filter, also called tapped delay line, that implements an all-zero
transfer function with a canonic direct form realization without feedback. For this
realization, the output signal y(n) is a linear combination of the filter coefficients, that

14

yields a quadratic mean-square error (MSE = E[|e(n)|2]) function with a unique
optimal solution. Other alternative adaptive FIR realizations are also used in order to
obtain improvements as compared to the transversal filter structure, in terms of
computational complexity, speed of convergence and finite word-length properties.
Adaptive IIR filter realizations: The most widely used realization of adaptive IIR
filters is the canonic direct form realization [42], due to its simple implementation and
analysis. However, there are some inherent problems related to recursive adaptive
filters which are structure dependent such as pole-stability monitoring requirement
and slow speed of convergence. To address these problems, different realizations
were proposed attempting to overcome the limitations of the direct form structure.
(c) Algorithm: The algorithm is the procedure used to adjust the adaptive filter
coefficients in order to minimize a prescribed criterion. The algorithm is determined by
defining the search method (or minimization algorithm), the objective function and the nature
of error signal. The choice of the algorithm determines several crucial aspects of the overall
adaptive process, such as existence of sub-optimal solutions, biased optimal solution and
computational complexity.

x(n)

w0

Z‐1

⊗

x(n-1)

w1

Z-1

Z-1

⊗

wN-1

⊕
y(n)

⊕

_
e(n)

d(n)

+

Fig.3.2. Transversal FIR filter architecture

15

x(n-N+1)

⊗

3.1.2 Adaptive Noise Canceller (ANC)
The goal of adaptive noise cancellation system is to reduce the noise portion and to
obtain the uncorrupted desired signal. In order to achieve this task, a reference of the noise
signal is needed. That reference is fed to the system, and it is called a reference signal x(n).
However, the reference signal is typically not the same signal as the noise portion of the
primary signal; it can vary in amplitude, phase or time. Therefore, the reference signal cannot
be simply subtracted from the primary signal to obtain the desired portion at the output.

Signal
Source

Noise
Source

s(n)

Primary Input

d(n)

x1(n)

Reference Input
x(n)

Adaptive
Filter

+

Σ

e(n)

Output

_

y(n)

Adaptive Noise Canceller

Fig.3.3. Block diagram for Adaptive Noise Canceller

Consider the Adaptive Noise Canceller (ANC) shown in Fig.3.3 [1]. The ANC has
two inputs: the primary input d(n), which represents the desired signal corrupted with
undesired noise and the reference input x(n), which is the undesired noise to be filtered out of
the system. The primary input therefore comprises of two portions: - first, the desired signal
and the other one is noise signal corrupting the desired portion of the primary signal.
The basic idea for the adaptive filter is to predict the amount of noise in the primary
signal and then subtract that noise from it. The prediction is based on filtering the reference
signal x(n), which contains a solid reference of the noise present in the primary signal. The
noise in the reference signal is filtered to compensate for the amplitude, phase and time delay
and then subtracted from the primary signal. The filtered noise represented by y(n) is the
system’s prediction of the noise portion of the primary signal and is subtracted from desired
signal d(n) resulting in a signal called error signal e(n), and it presents the output of the
system. Ideally, the resulting error signal should be only the desired portion of the primary
signal.

16

In practice, it is difficult to achieve this, but it is possible to significantly reduce the
amount of noise in the primary signal. This is the overall goal of the adaptive filters. This
goal is achieved by constantly changing (or adapting) the filter coefficients (weights). The
adaptation rules determine their performance and the requirements of the system used to
implement the filters.
A good example to illustrate the principles of adaptive noise cancellation is the noise
removal from the pilot’s microphone in the airplane. Due to the high environmental noise
produced by the airplane engine, the pilot’s voice in the microphone gets distorted with a
high amount of noise and is very difficult to comprehend. In order to overcome this problem,
an adaptive filter can be used. In this particular case, the desired signal is the pilot’s voice.
This signal is corrupted with the noise from the airplane’s engine. Here, the pilot’s voice and
the engine noise constitute primary signal d(n). Reference signal for the application would be
a signal containing only the engine noise, which can be easily obtained from the microphone
placed near the engine. This signal would not contain the pilot’s voice, and for this
application it is the reference signal x(n).
Adaptive filter shown in Fig.3.3 can be used for this application. The filter output y(n)
is the system’s estimate of the engine noise as received in the pilot’s microphone. This
estimate is subtracted from the primary signal (pilot’s voice plus engine noise), and at the
output of the system e(n) should contain only the pilot’s voice without any noise from the
airplane’s engine. It is not possible to subtract the engine noise from the pilot’s microphone
directly, since the engine noise received in the pilot’s microphone and the engine noise
received in the reference microphone are not the same signal. There are differences in
amplitude and time delay. Also, these differences are not fixed. They change in time with
pilot’s microphone position with respect to the airplane engine, and many other factors.
Therefore, designing the fixed filter to perform the task would not obtain the desired results.
The application requires adaptive solution.
There are many forms of the adaptive filters and their performance depends on the
objective set forth in the design. Theoretically, the major goal of any noise cancelling system
is to reduce the undesired portion of the primary signal as much as possible, while preserving
the integrity of the desired portion of the primary signal.

17

As noted above, the filter produces estimate of the noise in the primary signal
adjusted for magnitude, phase and time delay. This estimate is then subtracted from the noise
corrupted primary signal to obtain the desired signal. For the filter to work well, the adaptive
algorithm has to adjust the filter coefficients such that output of the filter is a good estimate
of the noise present in the primary signal.
To determine the amount by which noise in the primary signal is reduced, the mean
squared error technique is used. The Minimum Mean Squared Error (MMSE) is defined as
[42]:
min E[d (n) − XW T ] 2 = min E[(d (n) − y (n)) 2 ]

(3.1)

where d is the desired signal, X and W are the vectors of the input reference signal and
the filter coefficients respectively. This represents the measure of how well the newly
constructed filter (given as a convolution product y(n) = XW) estimates the noise present in
the primary signal. The goal is to reduce this error to a minimum. Therefore, the algorithms
that perform adaptive noise cancellation are constantly searching for a coefficient vector W,
which produces the minimum mean squared error.
Minimizing the mean squared of the error signal minimizes the noise portion of the
primary signal but not the desired portion. To understand this principle, recall that the
primary signal is made of the desired portion and the noise portion. The filtered reference
signal y(n) is a reference of the noise portion of the primary signal and therefore is correlated
with it. However, the reference signal is not correlated with the desired portion of the primary
signal. Therefore, minimizing the mean squared of the error signal minimizes only the noise
in the primary signal. This principle can be mathematically described as follows:
If we denote the desired portion of primary signal with s(n), and the noise portion of
desired signal as x1(n), it follows that d(n) = s(n) + x1(n). As shown in Fig.3.3, the output of
the system can be written as [43]:
e(n) = d (n) − y (n)

(3.2)

e ( n ) = s ( n ) + x1 ( n ) − y ( n )

e(n) 2 = s (n) 2 + (( x1 (n) − y (n)) 2 + 2 s (n)(( x1 (n) − y (n))
E[e(n) 2 ] = E[ s (n) 2 ] + (( x1 (n) − y (n)) 2 + 2 s (n)(( x1 (n) − y (n))

18

E[e(n) 2 ] = E[ s (n) 2 ] + E[(( x1 (n) − y (n)) 2 ] + 2 E[ s (n)(( x1 (n) − y (n))]

(3.3)

Due to the fact that the s(n) is un-correlated to both x1(n) and y(n), as noted earlier, the
last term is equal to zero, so we have
E[e(n) 2 ] = E[ s (n) 2 ] + E[(( x1 (n) − y (n)) 2 ]
min E[e(n) 2 ] = min E[ s(n) 2 ] + min E[(( x1 (n) − y (n))2 ]

(3.4)

and since s(n) is independent of W, we have
min E[e(n) 2 ] = E[ s (n) 2 ] + min E[(( x1 (n) − y (n)) 2 ]

(3.5)

Therefore, minimizing the error signal, minimizes the mean squared of the difference
between the noise portion of the primary signal x1(n), and the filter output y(n) .

3.2

Approaches to Adaptive Filtering Algorithms
Basically two approaches can be defined for deriving the recursive formula for the

operation of Adaptive Filters. They are as follows:
(i) Stochastic Gradient Approach: In this approach to develop a recursive algorithm for

updating the tap weights of the adaptive transversal filter, the process is carried out in two
stages. First we use an iterative procedure to find the optimum Wiener solution [43]. The
iterative procedure is based on the method of steepest descent. This method requires the
use of a gradient vector, the value of which depends on two parameters: the correlation
matrix of the tap inputs in the transversal filter and the cross-correlation vector between
the desired response and the same tap inputs. Secondly, instantaneous values for these
correlations are used to derive an estimate for the gradient vector. Least Mean Squared
(LMS) and Normalized Least Mean Squared (NLMS) algorithms lie under this approach
and are discussed in subsequent sections.
(ii) Least Square Estimation: This approach is based on the method of least squares.

According to this method, a cost function is minimized that is defined as the sum of
weighted error squares, where the error is the difference between some desired response
and actual filter output. This method is formulated with block estimation in mind. In
block estimation, the input data stream is arranged in the form of blocks of equal length
(duration) and the filtering of input data proceeds on a block by block basis, which
requires a large memory for computation. The Recursive Least Square (RLS) algorithm

19

falls under this approach and is discussed in subsequent section.

3.2.1

Least Mean Square (LMS) Algorithm
The Least Mean Square (LMS) algorithm [1] was first developed by Widrow and

Hoff in 1959 through their studies of pattern recognition [42]. Thereon it has become one of
the most widely used algorithm in adaptive filtering. The LMS algorithm is a type of adaptive
filter known as stochastic gradient-based algorithm as it utilizes the gradient vector of the
filter tap weights to converge on the optimal wiener solution. It is well known and widely
used due to its computational simplicity. With each iteration of the LMS algorithm, the filter
tap weights of the adaptive filter are updated according to the following formula:

w( n + 1) = w( n) + 2 μe( n ) x ( n)

(3.6)

where x(n) is the input vector of time delayed input values, and is given by
x(n) = [ x(n) x(n − 1) x(n − 2)....x(n − N + 1)]T

(3.7)

w( n) = [ w0 ( n) w1 ( n) w2 ( n)....w N −1 (n)]T represents the coefficients of the adaptive FIR

filter tap weight vector at time n and μ is known as the step size parameter and is a small
positive constant.
The step size parameter controls the influence of the updating factor. Selection of a
suitable value for μ is imperative to the performance of the LMS algorithm. If the value of μ
is too small, the time an adaptive filter takes to converge on the optimal solution will be too
long; if the value of μ is too large the adaptive filter becomes unstable and its output diverges
[14], [15], [22].
3.2.1.1 Derivation of the LMS Algorithm

The derivation of the LMS algorithm builds upon the theory of the wiener solution for
the optimal filter tap weights, w0, as outlined above. It also depends on the steepest descent
algorithm that gives a formula which updates the filter coefficients using the current tap
weight vector and the current gradient of the cost function with respect to the filter tap weight
coefficient vector, ξ(n).
w(n + 1) = w(n) − μ∇ξ ( n)

(3.8)

20

where

ξ (n) = E[e 2 (n)]

(3.9)

As the negative gradient vector points in the direction of steepest descent for the N
dimensional quadratic cost function each recursion shifts the value of the filter coefficients
closer towards their optimum value which corresponds to the minimum achievable value of
the cost function, ξ(n). The LMS algorithm is a random process implementation of the
steepest descent algorithm, from Eq. (3.9). Here the expectation for the error signal is not
known so the instantaneous value is used as an estimate. The gradient of the cost function,
ξ(n) can alternatively be expressed in the following form:
∇ξ (n) = ∇(e 2 (n))
= ∂e 2 (n) / ∂w
= 2e(n)∂e(n) / ∂w
= 2e( n)∂[d ( n) − y ( n)] / ∂w

= −2e(n)∂ewT (n).x(n)] / ∂w
= −2 e ( n ) x ( n )

(3.10)

Substituting this into the steepest descent algorithm of Eq. (3.9), we arrive at the
recursion for the LMS adaptive algorithm.
w( n + 1) = w( n) + 2 μe( n) x ( n)

(3.11)

3.2.1.2 Implementation of the LMS Algorithm

For the Implementation of each iteration of the LMS algorithm requires three distinct
steps in the following order:
1. The output of the FIR filter, y(n) is calculated using Eq. (3.12).
N −1

y (n) = ∑ w( n)x(n − i ) = wT (n) x(n)

(3.12)

i =0

2. The value of the error estimation is calculated using Eq. (3.13).

21

e( n ) = d ( n ) − y ( n )

(3.13)

3. The tap weights of the FIR vector are updated in preparation for the next iteration, by
Eq. (3.14).
w( n + 1) = w( n) + 2 μe( n) x ( n)

(3.14)

The main reason for the popularity of LMS algorithms in adaptive filtering is its
computational simplicity that makes its implementation easier than all other commonly used
adaptive algorithms. For each iteration, the LMS algorithm requires 2N additions and 2N+1
multiplications (N for calculating the output, y(n), one for 2μe(n) and an additional N for the
scalar by vector multiplication) .

3.2.2

Normalized Least Mean Square (NLMS) Algorithm
In the standard LMS algorithm when the convergence factor μ is large, the algorithm

experiences a gradient noise amplification problem. In order to solve this difficulty we can
use the NLMS algorithm [14]-[17]. The correction applied to the weight vector w(n) at
iteration n+1 is “normalized” with respect to the squared Euclidian norm of the input vector
x(n) at iteration n. We may view the NLMS algorithm as a time-varying step-size algorithm,
calculating the convergence factor μ as in Eq. (3.15)[10].

μ ( n) =

α
c + x ( n)

(3.15)

2

where α is the NLMS adaption constant, which optimize the convergence rate of the
algorithm and should satisfy the condition 0<α<2, and c is the constant term for
normalization and is always less than 1.
The Filter weights are updated by the Eq. (3.16).
w(n + 1) = w(n) +

α
c + x ( n)

2

e( n ) x ( n )

(3.16)

It is important to note that given an input data (at time n) represented by the input
vector x(n) and desired response d(n), the NLMS algorithm updates the weight vector in such
a way that the value w(n+1) computed at time n+1 exhibits the minimum change with respect

22

to the known value w(n) at time n. Hence, the NLMS is a manifestation of the principle of
minimum disturbance [3].
3.2.2.1 Derivation of the NLMS Algorithm

This derivation of the normalized least mean square algorithm is based on FarhangBoroujeny and Diniz [43]. To derive the NLMS algorithm we consider the standard LMS
recursion in which we select a variable step size parameter, μ(n). This parameter is selected
so that the error value, e+(n), will be minimized using the updated filter tap weights, w(n+1),
and the current input vector, x(n).

w(n + 1) = w(n) + 2 μ (n)e(n) x(n)
e + (n) = d (n) − wT (n + 1) x(n)
= (1 − 2 μ (n) xT (n) x(n))e(n)

(3.17)

Next we minimize (e+(n))2, with respect to μ(n). Using this we can then find a value
for µ(n) which forces e+(n) to zero.

μ ( n) =

1
2 x ( n ) x ( n)

(3.18)

T

This μ(n) is then substituted into the standard LMS recursion replacing μ, resulting in
the following.
w(n + 1) = w(n) + 2 μ (n)e(n) x(n)
1
w(n + 1) = w(n) + T
e( n) x ( n)
x ( n) x ( n)

w(n + 1) = w(n ) + μ (n) x(n )

(3.19)

, where μ (n) =

α
x x+c
T

(3.20)

Often the NLMS algorithm as expressed in Eq. (3.20 is a slight modification of the
standard NLMS algorithm detailed above. Here the value of c is a small positive constant in
order to avoid division by zero when the values of the input vector are zero. This was not
implemented in the real time as in practice the input signal is never allowed to reach zero due
to noise from the microphone and from the ADC on the Texas Instruments DSK. The
parameter α is a constant step size value used to alter the convergence rate of the NLMS
algorithm, it is within the range of 0<α<2, usually being equal to 1.

23

3.2.2.2 Implementation of the NLMS Algorithm

The NLMS algorithm is implemented in MATLAB as outlined later in Chapter 6. It is
essentially an improvement over LMS algorithm with the added calculation of step size
parameter for each iteration.
1. The output of the adaptive filter is calculated as:
N −1

y (n) = ∑ w( n)x(n − i ) = wT (n) x(n)

(3.21)

i =0

2. The error signal is calculated as the difference between the desired output and the filter
output given by:
e( n) = d ( n ) − y ( n)

(3.22)

3. The step size and filter tap weight vectors are updated using the following equations in
preparation for the next iteration:
For i=0,1,2,…….N-1

μ i ( n) =

α
c + xi ( n )

(3.23)

2

w(n + 1) = w(n) + μ i (n)e(n) xi (n)

(3.24)

where α is the NLMS adaption constant and c is the constant term for normalization.
With α =0.02 and c=0.001, each iteration of the NLMS algorithm requires 3N+1
multiplication operations.

3.2.3

Recursive Least Square (RLS) Algorithm
The other class of adaptive filtering technique studied in this thesis is known as

Recursive Least Squares (RLS) algorithm [42]-[44]. This algorithm attempts to minimize the
cost function in Eq. (3.25) where k=1 is the time at which the RLS algorithm commences and
λ is a small positive constant very close to, but smaller than 1. With values of λ<1, more
importance is given to the most recent error estimates and thus the more recent input samples,
that results in a scheme which emphasizes on recent samples of observed data and tends to
forget the past values.

24

n

2
ξ ( n) = ∑ λ n − k e n ( k )

(3.25)

k =1

Unlike the LMS algorithm and NLMS algorithm, the RLS algorithm directly
considers the values of previous error estimations. RLS algorithm is known for excellent
performance when working in time varying environments. These advantages come at the cost
of an increased computational complexity and some stability problems.
3.2.3.1 Derivation of the RLS Algorithm

The RLS cost function of Eq. (3.25) shows that at time n, all previous values of the
estimation error since the commencement of the RLS algorithm are required. Clearly, as time
progresses the amount of data required to process this algorithm increases. Limited memory
and computation capabilities make the RLS algorithm a practical impossibility in its purest
form. However, the derivation still assumes that all data values are processed. In practice
only a finite number of previous values are considered, this number corresponds to the order
of the RLS FIR filter, N.
First we define yn(k) as the output of the FIR filter, at n, using the current tap weight
vector and the input vector of a previous time k. The estimation error value en(k) is the
difference between the desired output value at time k and the corresponding value of yn(k).
These and other appropriate definitions are expressed below, for k=1,2, 3,., n.
yn (k ) = wT (n) x(k )
en (k ) = d (k ) − yn (k )
d (n) = [d (1), d (2).....d (n)]T
y (n) = [ yn (1), yn (2)..... yn (n)]T
e(n) = [en (1), en (2).....en (n)]T
e( n ) = d ( n ) − y ( n )

(3.26)

If we define X(n) as the matrix consisting of the n previous input column vector up to
the present time then y(n) can also be expressed as Eq. (3.27).
X (n) = [ x(1), x(2),....... x( n)]

y (n) = X T (n) w(n)

(3.27)

25

The cost function can be expressed in matrix vector form using a diagonal matrix,
Λ(n) consisting of the weighting factors.
n

2
ξ ( n) = ∑ λ n − k e n ( k )
k =1

~
= eT (n)Λ (n)e(n)
⎡ λn −1
⎢
⎢ 0
~
where Λ (n) = ⎢ 0
⎢
⎢ ...
⎢ 0
⎣

0

λ

n−2

0
0

λn −3

0
...
0

...
0

0
0
0
...
0

0
0
0
...
1

⎤
⎥
⎥
⎥
⎥
⎥
⎥
⎦

(3.28)

Substituting values from Eq. (3.26) and (3.27), the cost function can be expanded and
then reduced as in Eq. (3.29). (Temporarily dropping (n) notation for clarity).

~

ξ ( n ) = eT ( n ) Λ ( n ) e ( n )

~
~
~
~
= d T Λd − d T Λy − y T Λd + yT Λy
~
~
~
~
= d T Λd − d T Λ ( X T w) − ( X T w)T Λd + ( X T w)T Λ ( X T w)
~
~
~
= d T Λd − 2θ w + wTψ w
λ

λ

(3.29)

where
~
~
ψ λ = X ( n) Λ ( n) X T ( n)
~
~
θ λ = X ( n) Λ ( n) d ( n)
We derive the gradient of the above expression for the cost function with respect to
the filter tap weights. By forcing this to zero we find the coefficients for the filter w(n), which
minimizes the cost function.
~
~
ψ λ (n) w(n) = θ λ (n)
~ −1 ~
w(n) = ψ λ (n)θ λ (n)

(3.30)

The matrix Ψ(n) in the above equation can be expanded and rearranged in recursive
form. We can use the special form of the matrix inversion lemma to find an inverse for this
matrix which is required to calculate the tap weight vector update. The vector k(n) is known
as the gain vector and is included in order to simplify the calculation.

26

~−
~−
ψ λ 1 (n) = λψ λ 1 (n − 1) + x(n) xT (n)
~−
= λ−1ψ λ 1 (n − 1) −

~−
~−
λ− 2ψ λ 1 (n − 1) x(n) xT (n)ψ λ 1 (n − 1)
~−
1 + λ−1 xT (n)ψ λ 1 (n − 1) x(n)

~−
~−
= λ−1 (ψ λ 1 (n − 1) − k (n) xT (n)ψ λ 1 (n − 1))
where
~−
λ−1ψ λ 1 (n − 1) x(n)
~−
1 + λ−1 xT (n)ψ λ 1 (n − 1) x(n)

k ( n) =

~−
= ψ λ 1 ( n) x ( n)

(3.31)

The vector θλ(n) of Eq. (3.29) can also be expressed in a recursive form. Using this
and substituting Ψ-1(n) from equation (3.31) into Eq. (3.30) we can finally arrive at the filter
weight update vector for the RLS algorithm, as in Eq. (3.32).
~
~
θ λ (n) = λθ λ (n − 1) + x(n)d (n)
~ −1 ~
w (n) = ψ (n)θ (n)
λ

~
=ψ

λ

λ

−1

~
~
~ −1
(n − 1)θ λ (n − 1) − k (n) xTψ λ (n − 1)θ λ (n − 1) + k (n)d (n)

= w (n − 1) − k (n) xT (n) w (n − 1) + k (n)d (n)
= w (n − 1) + k (n)(d (n) − w T (n − 1) x(n))
w (n) = w (n − 1) + k (n)en −1 (n)

(3.32)

where en −1 (n) = d (n) − w T (n − 1) x(n)
3.2.3.2 Implementation of the RLS Algorithm:

As stated previously, the memory of the RLS algorithm is confined to a finite number
of values corresponding to the order of the filter tap weight vector. Two factors of the RLS
implementation must be noted: first, although matrix inversion is essential for derivation of
the RLS algorithm, no matrix inversion calculations are required for the implementation; thus
greatly reducing the amount of computational complexity of the algorithm. Secondly, unlike
the LMS based algorithms, current variables are updated within the iteration they are to be
used using values from the previous iteration.
To implement the RLS algorithm, the following steps are executed in the following
order:
1. The filter output is calculated using the filter tap weights from the previous iteration and
the current input vector.
yn −1 (n) = w T (n − 1) x(n)

(3.33)

27

2. The intermediate gain vector is calculated using Eq. (3.34).
−1
u (n) = wλ (n − 1) x(n)
k (n) = u (n) /(λ + x T (n)u (n))

(3.34)

3. The estimation error value is calculated using Eq. (3.35).
en −1 (n) = d (n) − yn −1 (n)

(3.35)

4. The filter tap weight vector is updated using Eq. (3.36) and the gain vector calculated
in Eq. (3.34).
w(n) = w T (n − 1) + k (n)en −1 (n)

(3.36)

5. The inverse matrix is calculated using Eq. (3.37).

ψ λ −1 ( n) = λ −1 (ψ λ −1 ( n − 1) − k ( n)[ x T ( n)ψ λ −1 ( n − 1)]

(3.37)

When we calculate for each iteration of the RLS algorithm, it requires 4N2
multiplication and 3N2 addition operations.

3.3

Adaptive Filtering using MATLAB
MATLAB is the acronym of Matrix Laboratory was originally designed to serve as

the interactive link to the numerical computation libraries LINPACK and EISPACK that
were used by engineers and scientists when they were dealing with sets of equations. The
MATLAB software was originally developed at the University of New Mexico and Stanford
University in the late 1970s. By 1984, a company was established named as Matwork by Jack
Little and Cleve Moler with the clear objective of commercializing MATLAB. Over a million
engineers and scientists use MATLAB today in well over 3000 universities worldwide and it
is considered a standard tool in education, business, and industry.
The basic element in MATLAB is the matrix and unlike other computer languages it
does not have to be dimensioned or declared. MATLAB’s main objective was to solve
mathematical problems in linear algebra, numerical analysis, and optimization but it quickly
evolved as the preferred tool for data analysis, statistics, signal processing, control systems,
economics, weather forecast, and many other applications. Over the years, MATLAB has
evolved creating an extended library of specialized built-in functions that are used to generate
among other things two-dimensional (2-D) and 3-D graphics and animation and offers

28

numerous supplemental packages called toolboxes that provide additional software power in
special areas of interest such as•

Curve fitting

•

Optimization

•

Signal processing

•

Image processing

•

Filter design

•

Neural network design

•

Control systems

MATLAB
Stand alone
Application

Simulink

Application
Development

Stateflow
Toolboxes
Blocksets
Data
Sources

Data Access Tools
Student
Products

Code Generation
Tools
Mathworks Partner
Products

C Code

Fig.3.4. MATLAB versatility diagram

The MATLAB is an intuitive language and offers a technical computing environment.
It provides core mathematics and advance graphical tools for data analysis visualization and
algorithm and application development. The MATLAB is becoming a standard in industry,
education, and business because the MATLAB environment is user-friendly and the objective
of the software is to spend time in learning the physical and mathematical principles of a
problem and not about the software. The term friendly is used in the following sense: the
MATLAB software executes one instruction at a time. By analyzing the partial results and
based on these results, new instructions can be executed that interact with the existing
information already stored in the computer memory without the formal compiling required by
other competing high-level computer languages.

29

Major Software Characteristics:
i.

Matrix based numeric computation.

ii.

High level programming language.

iii.

Toolboxes provide application-specific functionality.

iv.

Multiple Platform Support.

v.

Open and Extensible System Architecture.

vi.

Interfaces to other language (C, FORTRAN etc).
For the simulation of the algorithms discussed in sec.3.2 MATLAB Version

7.4.0.287(R2007a) software is used. In the experimental setup, first of all high level
MATLAB programs [5],[20] are written for LMS , NLMS and RLS algorithms as per the
implementation steps described in sec.3.2.1.2, sec.3.2.2.2 and sec. 3.2.3.2 respectively [44] .
Then the simulation of above algorithms is done with a noisy tone signal generated through
MATLAB commands (refer sec. 6.1). The inputs to the programs are; the tone signal as
primary input s(n), random noise signal as reference input x(n), order of filter (N), step size
value (µ) ,number of iterations (refer Fig. 6.1) whereas the outputs are: the filtered output and
MSE which can be seen in the graphical results obtained after simulation gets over( refer
Fig.6.2).
The output results for the MATLAB simulation of LMS, NLMS and RLS algorithm
are presented and discussed later in the chapter-6.

30

Chapter-4

SIMULINK MODEL DESIGN FOR HARDWARE IMPLEMENTATION
4.1

Introduction to Simulink
Simulink is a software package for modeling, simulating and analyzing dynamic

systems [46]. It supports linear and nonlinear systems modeled in continuous time, sampled
time, or a hybrid of the two. Systems can also be multi rate, i.e. have different parts that are
sampled or updated at different rates. For modeling, simulink provides a graphical user
interface (GUI) for building models as block diagrams, using click-and-drag mouse
operations. With this interface, we can draw the models just as we would with pencil and
paper (or as most textbooks depict them). Simulink includes a comprehensive block library of
sinks, sources, linear and nonlinear components, and connectors. We can also customize and
create our own blocks.
Models are hierarchical, so we can build models using both top-down and bottom-up
approaches. We can view the system at a high level and then double-click blocks to go down
through the levels and thus visualize the model details. This approach provides insight into
how a model is organized and how its parts interact. After we define a model, we can
simulate it using a choice of integration methods either from the simulink menu or by
entering commands in the MATLAB command window.
In simulink, the menu is particularly convenient for interactive work. The command
line approach is very useful for running a batch of simulations (for example, if we want to
sweep a parameter across a range of values). Using scopes and other display blocks, we can
see the simulation results while the simulation is running. In addition, we can change many
parameters and see what happens. The simulation results can be put in the MATLAB
workspace for post processing and visualization.
The simulink model can be applied for modeling various time-varying systems that
includes control systems, signal processing systems, video processing systems, image
processing systems, communication and satellite systems, ship systems, automotive systems,
monetary systems, aircraft & spacecraft dynamics systems, and biological systems as
illustrated in Fig.4.1.

31

Fig.4.1. Simulink Applications

4.2

Model Design
In the experimental setup for noise cancellation, simulink tool box has been used

which provides the capability to model a system and to analyze its behavior. Its library is
enriched with various functions which mimics the real system. The designed model for
Adaptive Noise Cancellation (ANC) using simulink toolbox is shown in Fig.4.2.

4.2.1 Common Blocks used in Building Model
4.2.1.1 C6713 DSK ADC Block

This block is used to capture and digitize analog signals from external sources such as
signal generators, frequency generators or audio devices. Dragging and dropping C6713 DSK
ADC block in simulink block diagram allows audio coder-decoder module (codec) on the
C6713 DSK to convert an analog input signal to a digital signal for the digital signal
processing. Most of the configuration options in the block affect the codec. However, the
output data type, samples per frame and scaling options are related to the model that we are
using in simulink.

32

Fig.4.2. Adaptive Noise Cancellation Simulink model

4.2.1.2 C6713 DSK DAC Block

Simulink model provides the means to generate output of an analog signal through the
analog output jack on the C6713 DSK. When C6713 DSK DAC block is added to the model,
the digital signal received by the codec is converted to an analog signal. Codec sends signal
to the output jack after converting the digital signal to analog form using digital-to-analog
conversion (D/A).
4.2.1.3 C6713 DSK Target Preferences Block

This block provides access to the processor hardware settings that need to be
configured for generating the code from Real-Time Workshop (RTW) to run on the target. It
is mandatory to add this block to the simulink model for the embedded target C6713. This
block is located in the Target Preferences in Embedded Target for TI C6000 DSP for TI DSP
library.
4.2.1.4 C6713 DSK Reset Block

This block is used to reset the C6713 DSK to initial conditions from the simulink
model. Double-clicking this block in a simulink model window resets the C6713 DSK that is
running the executable code built from the model. When we double-click the Reset block, the

33

block runs the software reset function provided by CCS that resets the processor on C6713
DSK. Applications running on the board stop and the signal processor returns to the initial
conditions that we defined.
4.2.1.5 NLMS Filter Block

This block adapts the filter weights based on the NLMS algorithm for filtering the
input signal. We select the adapt port check box to create an adapt port on the block. When
the input to this port is nonzero, the block continuously updates the filter weights. When the
input to this port is zero, the filter weights remain constant. If the reset port is enabled and a
reset event occurs, the block resets the filter weights to their initial values.
4.2.1.6 C6713 DSK LED Block

This block triggers the entire three user LEDs located on the C6711 DSK. When we
add this block to a model and send a real scalar to the block input, the block sets the LED
state based on the input value it receives: When the block receives an input value equal to 0,
the LEDs are turned OFF. When the block receives a nonzero input value, the LEDs are
turned ON.
4.2.1.7 C6713 DSK DIP Switch Block

Outputs state of user switches located on C6713 DSK board. In boolean mode,
output is a vector of 4 Boolean values, with the least-significant bit (LSB) first. In Integer
mode, output is an integer from 0 to 15. For simulation, checkboxes in the block dialog are
used in place of the physical switches.

4.2.2 Building the Model
To create the model, first type simulink in the MATLAB command window or
directly click on the shortcut icon

. On Microsoft Windows, the simulink library browser

appears as shown in Fig. 4.3.

34

Fig.4.3. Simulink library browser

To create a new model, select Model from the New submenu of the simulink library
window's File menu. To create a new model on Windows, select the New Model button on
the Library Browser's toolbar.
Simulink opens a new model window like Fig. 4.4.

35

Fig.4.4. Blank new model window

To create Adaptive Noise Cancellation (ANC) model, we will need to copy blocks
into the model from the following simulink block libraries:
•

Target for TI C6700 library (ADC, DAC, DIP, and LED blocks)

•

Signal processing library (NLMS filter block)

•

Commonly used blocks library (Constant block, Switch block and Relational block)

•

Discrete library (Delay block)
To copy the ADC block from the Library Browser, first expand the Library Browser

tree to display the blocks in the Target for TI C6700 library. Do this by clicking on the library
node to display the library blocks. Then select the C6713 DSK board support sub library and
finally, click on the respective block to select it.
Now drag the ADC block from the browser and drop it in the model window.
Simulink creates a copy of the blocks at the point where you dropped the node icon as
illustrated in Fig.4.5.

36

Fig.4.5. Model window with ADC block

Copy the rest of the blocks in a similar manner from their respective libraries into the
model window. We can move a block from one place to another place by dragging the block
in the model window. We can move a block a short distance by selecting the block and then
pressing the arrow keys. With all the blocks copied into the model window, the model should
look something like Fig.4.6.
If we examine the block icons, we see an angle bracket on the right of the ADC block
and two on the left of the NLMS filter block. The > symbol pointing out of a block is an
output port; if the symbol points to a block, it is an input port. A signal travels out of an
output port and into an input port of another block through a connecting line. When the
blocks are connected, the port symbols disappear.
Now it's time to connect the blocks. Position the pointer over the output port on the
right side of the ADC block and connect it to the input port of delay, NLMS filter and switch
block. Similarly make all connection as in Fig.4.2.

4.3

Model Reconfiguration
Once the model is designed we have to reconfigure the model as per the requirement

of the desired application. The simulink blocks parameters are adjusted as per the input
output devices used. The input devices may be function generator or microphone and the
output devices may be DSO or headphone respectively. This section explains and illustrates
the reconfiguration setting of each simulink block like ADC, DAC, Adaptive filter, DIP,

37

LED, relational operator, switch block, and all that are used in the design of adaptive noise
canceller.

Fig.4.6. Model illustration before connections

4.3.1 The ADC Settings
This block can be reconfigured to receive the input either from microphone or
function generator. Input is applied through microphone when ADC source is kept at “Mic
In” and through function generator when ADC source is kept at “Line In” as shown in
Fig.4.7. The other settings are as follows:
Double-click on the blue box to the left marked “DSK6713 ADC”.
The screen as shown in Fig.4.7 will appear.
Change the “ADC source” to “Line In” or “Mic In”.
If we have a quiet microphone, select “+20dB Mic gain boost”.
Set the “Sampling rate (Hz)” to “48 kHz”.
Set the “Samples per frame” to 64.
When done, click on “OK”.
Important: Make sure the “Stereo” box is empty.

38

4.3.2 The DAC Settings
The DAC setting needs to be matched to those of the ADC. The major parameter is
the sampling rate that is kept at the same rate of ADC i.e. 48 kHz as shown in Fig.4.8.

Fig.4.7. Setting up the ADC for mono microphone input

Fig.4.8. Setting the DAC parameters

39

4.3.3 NLMS Filter Parameters Settings
The most critical variable in an NLMS filter is the initial setup of “Step size (mu)”. If
“mu” is too small, the filter has very fine resolution but reacts too slowly to the input signal.
If “mu” is too large, the filter reacts very quickly but the error also remains large. The major
parameters values that we have to change for the designed model are (shown in Fig.4.9): Step
size (mu) = 0.001, Filter length =19
Select the Adapt port check box to create an Adapt port on the block. When the input
to this port is nonzero, the block continuously updates the filter weights. When the input to
this port is zero, the filter weights remain constant.

Fig.4.9. Setting the NLMS filter parameters

40

4.3.4 Delay Parameters Settings
Delay parameter is required to delay the discrete-time input signal by a specified
number of samples or frames. Because we are working with frames of 64 samples, it is
convenient to configure the delay using frames. The steps for setting are described below and
are illustrated in Fig. 4.10.
Double-click on the “Delay” block.
Change the “Delay units” to Frames.
Set the “Delay (frames)” to 1. This makes the delay 64 samples.

Fig.4.10. Setting the delay unit

4.3.5 DIP Switches Settings
DIP switches are manual electric switches that are packaged in a group in a standard
dual in-line package (DIP).These switches can work in two modes; Boolean mode, Integer
mode. In Boolean mode, outputs are a vector of 4 boolean values with the least-significant bit
(LSB) first. In Integer mode, outputs are an integer from 0 to 15. The DIP switches needs to
be configured as shown in Fig. 4.11.

41

The “Sample time” should set to be “–1”.

Fig.4.11. Setting up the DIP switch values

4.3.6 Constant Value Settings
The switch values lie between 0 and 15. We will use switch values 0 and 1. For
settings, Double-click on the “Constant” block. Set the “Constant value” to 1 and the
“Sample time” to “inf” as shown in Fig.4.12.

Fig.4.12. Setting the constant parameters

42

4.3.7 Constant Data Type Settings
The signal data type for the constant used in ANC model is set to “int16” as shown in
Fig. 4.13. The setting of parameter can be done as follows:
Click on the “Signal Data Types” tab.
Set the “Output data type mode” to “int16”.
This is compatible with the DAC on the DSK6713.

Fig.4.13. Data type conversion to 16-bit integer

4.3.8 Relational Operator Type Settings
Relational operator is used to check the given condition for the input signal. The
relational operator setting for the designed model can be done as follows:
Double click on the “Relational Operator” block.
Change the “Relational operator” to “==”.
Click on the “Signal Data Types” tab.

4.3.9 Relational Operator Data Type Settings
Set the “Output data type mode” to “Boolean”.
Click on “OK”. ( refer Fig.4.14)

43

Fig.4.14. Changing the output data type

4.3.10 Switch Settings
The switch which is used in this model has three inputs viz. input 1, input 2 and input
3 numbered from top to bottom (refer Fig 4.2). The input 1 & input 3 are data inputs and
input 2 is the control input. When input 2 satisfies the selection criteria, input 1 is passed to
the output port otherwise input 3. The switch is configured as:
Double click on the “switch”
Set the criteria for passing first input to “u2>=Threshold”
Click “ok”

The simulink model for the hardware implementation of NLMS algorithm is
designed successfully and the designed model is reconfigured to meet the requirement of
TMS320C6713 DSP Processor environment. The reconfigured model shown in Fig.4.2 is
ready to connect with Code Composer Studio [50] and DSP Processor with the help of RTDX
link and Real-Time Workshop [47]. This is presented in chapter5.

44

Chapter-5

REAL-TIME IMPLEMENTATION ON DSP PROCESSOR
Digital signal processors are fast special-purpose microprocessors with a specialized
type of architecture and an instruction set appropriate for signal processing [45]. The
architecture of the digital signal processor is very well suited for numerically intensive
calculations. Digital signal processors are used for a wide range of applications which
includes communication, control, speech processing, image processing etc. These processors
have become the products of choice for a number of consumer applications, because they are
very cost-effective and can be reprogrammed easily for different applications.
DSP techniques have been very successful because of the development of low-cost
software and hardware support [48]. DSP processors are concerned primarily with real-time
signal processing. Real-time processing requires the processing to keep pace with some
external event, whereas non-real-time processing has no such timing constraint. The external
event is usually the analog input. Analog-based systems with discrete electronic components
such as resistors can be more sensitive to temperature changes whereas DSP-based systems
are less affected by environmental conditions.
In this chapter we will learn how we can realize or implement an adaptive filter on
hardware for real-time experiments. The model which was designed in previous chapter will
be linked to the DSP processor with help of Real Time Data Exchange (RTDX) utility
provided in simulink.

5.1

Introduction to Digital Signal Processor (TMS320C6713)
The TMS320C6713 is a low cost board designed to allow the user to evaluate the

capabilities of the C6713 DSP and develop C6713-based products [49]. It demonstrates how
the DSP can be interfaced with various kinds of memories, peripherals, Joint Text Action
Group (JTAG) and parallel peripheral interfaces.
The board is approximately 5 inches wide and 8 inches long as shown in Fig.5.2 and
is designed to sit on the desktop external to a host PC. It connects to the host PC through a
USB port. The processor board includes a C6713 floating-point digital signal processor and a

45

32-bit stereo codec TLV320AIC23 (AIC23) for input and output. The onboard codec AIC23
uses a sigma–delta technology that provides ADC and DAC. It connects to a 12-MHz system
clock. Variable sampling rates from 8 to 96 kHz can be set readily [51].
A daughter card expansion is also provided on the DSK board. Two 80-pin connectors
provide for external peripheral and external memory interfaces. The external memory
interface (EMIF) performs the task of interfacing with the other memory subsystems. Lightemitting diodes (LEDs) and liquid-crystal displays (LCDs) are used for spectrum display.
The DSK board includes 16MB (Megabytes) of synchronous dynamic random access
memory (SDRAM) and 256kB (Kilobytes) of flash memory.
Four connectors on the board provide inputs and outputs: MIC IN for microphone
input, LINE IN for line input, LINE OUT for line output, and HEADPHONE for a
headphone output (multiplexed with line output). The status of the four users DIP switches on
the DSK board can be read from a program and provides the user with a feedback control
interface (refer Fig.5.1 & Fig.5.2). The DSK operates at 225MHz.Also onboard are the
voltage regulators that provide 1.26 V for the C6713 core and 3.3V for its memory and
peripherals.
The major DSK hardware features are:
A C6713 DSP operating at 225 MHz.
An AIC23 stereo codec with Line In, Line Out, MIC, and headphone stereo jacks.
16 Mbytes of synchronous DRAM (SDRAM).
512 Kbytes of non-volatile Flash memory (256 Kbytes usable in default
configuration).
Four user accessible LEDs and DIP switches.
Software board configuration through registers implemented in complex logic device.
Configurable boot options.
Expansion connectors for daughter cards.
JTAG emulation through onboard JTAG emulator with USB host interface or external
Emulator.
Single voltage power supply (+5V).

46

Fig.5.1. Block diagram of TMS320C6713 processor

Fig.5.2. Physical overview of the TMS320C6713 processor

47

5.1.1

Central Processing Unit Architecture
The CPU has Very Large Instruction Word (VLIW) architecture [53]. The CPU

always fetches eight 32-bit instructions at once and there is a 256-bit bus to the internal
program memory. Each group of eight instructions is called a fetch packet. The CPU has
eight functional units that can operate in parallel and are equally split into two halves, A and
B. All eight units do not have to be given instruction words if they are not ready. Therefore,
instructions are dispatched to the functional units as execution packets with a variable
number of 32-bit instruction words. The functional block diagram of Texas Instrument (TI)
processor architecture is shown below in Fig.5.3.
32

       EMIF
McASP1
McASP0

McBSP0
Pin Multiplexing

     I2C1
I2C0
Timer 1
Timer 0

Enhanced DMA Controller
(16 Channel)

McBSP1

L2 Cache
Memory
4 Banks
64K Bytes
Total

(Up to 4‐
way)

L2
Memory
192K
Bytes

C67x CPU
Instruction Fetch

Instruction Dispatch

Instruction Decode
Data Path A            Data Path B
A Register File       B Register
.L1 .S1 .M1 .D1

.D2 .M2 .S2 .L2

HPI

Control
Register
Control
Test
In‐Circuit
Emulation
Interrupt
Control

L1D Cache
2‐Way
Set Associative
4K Bytes
Clock Generator
Oscillator and PLL
×4 through ×25
Multiplier
/1 through /32 Divider

GPIO
16

LIP Cache
Direct Mapped
4 Bytes Total

Power –
Down Logic

Fig.5.3. Functional block diagram of TMS320C6713 CPU

The eight functional units include:
Four ALU that can perform fixed and floating-point operations (.L1, .L2, .S1, .S2).
Two ALU’s that perform only fixed-point operations (.D1, .D2).

48

Two multipliers that can perform fixed or floating-point multiplications (.M1, .M2).

5.1.2 General Purpose Registers Overview
The CPU has thirty two 32-bit general purpose registers split equally between the A
and B sides. The CPU has a load/store architecture in which all instructions operate on
registers. The data-addressing unit .D1 and .D2 are in charge of all data transfers between the
register files and memory. The four functional units on a side freely share the 16 registers on
that side. Each side has a single data bus connected to all the registers on the other side so
that functional units on one side can access data in the registers on the other side. Access to a
register on the same side uses one clock cycle while access to a register on the other side
requires two clock cycles i.e. read and write cycle.

5.1.3 Interrupts
The C6000 CPUs contain a vectored priority interrupt controller. The highest priority
interrupt is RESET which is connected to the hardware reset pin and cannot be masked. The
next priority interrupt is the NMI which is generally used to alert the CPU of a serious
hardware problem like a power failure. Then, there are twelve lower priority maskable
interrupts INT4–INT15 with INT4 having the highest and INT15 the lowest priority.

Fig.5.4. Interrupt priority diagram

49

The following Fig. 5.5 depicts how the processor handles an interrupt when it arrives.
Interrupt handling mechanism is a vital feature of microprocessor.

Fig.5.5. Interrupt handling procedure

These maskable interrupts can be selected from up to 32 sources (C6000 family). The
sources vary between family members. For the C6713, they include external interrupt pins
selected by the GPIO unit, and interrupts from internal peripherals such as timers, McBSP
serial ports, McASP serial ports, EDMA channels, and the host port interface. The CPUs
have a multiplexer called the interrupt selector that allows the user to select and connect
interrupt sources to INT4 through INT15.As soon as the interrupt is serviced, processor
resumes to the same operation which was under processing prior to interrupt request.

5.1.4 Audio Interface Codec
The C6713 uses a Texas AIC23 codec. In the default configuration, the codec is
connected to the two serial ports, McBSP0 and McBSP1. McBSP0 is used as a unidirectional
channel to control the codec's internal configuration registers. It should be programmed to
send a 16-bit control word to the AIC23 in SPI format. The top 7 bits of the control word
specify the register to be modified and the lower 9 bits contain the register value. Once the

50

codec is configured, the control channel is normally idle while audio data is being
transmitted. McBSP1 is used as the bi-directional data channel for ADC input and DAC
output samples. The codec supports a variety of sample formats. For the experiments in this
work, the codec should be configured to use 16-bit samples in two’s complement signed
format.
The codec should be set to operate in master mode so as to supply the frame
synchronization and bit clocks at the correct sample rate to McBSP1. The preferred serial
format is DSP mode which is designed specifically to operate with the McBSP ports on TI
DSPs. The codec has a 12 MHz system clock which is same as the frequency used in many
USB systems. The AIC23 can divide down the 12 MHz clock frequency to provide sampling
rates of 8000 Hz, 16000 Hz, 24000 Hz, 32000 Hz, 44100 Hz, 48000 Hz, and 96000 Hz.

DSK

DSP
CPU

McBSP

McBSP

AIC23

Fig.5.6. Audio connection illustrating control and data signal

The DSK uses two McBSPs to communicate with the AIC23 codec, one for control,
another for data. The C6713 supplies a 12 MHz clock to the AIC23 codec which is divided
down internally in the AIC23 to give the sampling rates. The codec can be set to these
sampling rates by using the function DSK6713_AIC23_setFreq (handle,freq ID) from the
BSL. This function puts the quantity “Value” into AIC23 control register 8. Some of the
AIC23 analog interface properties are:
The ADC for the line inputs has a full-scale range of 1.0 V RMS.

51

The microphone input is a high-impedance, low-capacitance input compatible with a
wide range of microphones.
The DAC for the line outputs has a full-scale output voltage range of 1.0 V RMS.
The stereo headphone outputs are designed to drive 16 or 32-ohm headphones.
The AIC23 has an analog bypass mode that directly connects the analog line inputs to
the analog line outputs.
The AIC23 has a side tone insertion mode where the microphone input is routed to the
line and headphone outputs.
AIC23 Codec

FSX1
CLKX1
TX1

CONTROL
SPI Format

CS
SCLK
SD IN

Digital

Control Registers

McBSP0

0
1
2
3
4
5
6
7
8
9
15

LEFT IN VOL
RIGHT IN VOL
LEFT HP VOL
RIGHT HP VOL
ANAPATH
DIGPATH
POWER DOWN
DIGIF
SAMPLE RATE
DIGACT
RESET

DATA

McBSP1
DR2
FX2
CLKR
CLKX
FSR2
DX2

D OUT
LRC OUT
B CLK
LRC IN
D IN

   MIC IN

   LINE IN

Analog

LINE OUT

MIC IN

ADC

LINE IN

DAC

LINE OUT
HP OUT

  HP OUT

Fig.5.7. AIC23 codec interface

5.1.5 DSP/BIOS & RTDX
The DSP/BIOS facilities utilize the Real-Time Data Exchange (RTDX) link to obtain
and monitor target data in real-time [47]. I utilized the RTDX link to create my own
customized interfaces to the DSP target by using the RTDX API Library. The RTDX
transfers data between a host computer and target devices without interfering with the target
application. This bi-directional communication path provides data collection by the host as
well as host interaction while running target application. RTDX also enables host systems to
provide data stimulation to the target application and algorithms.

52

Data transfer to the host occurs in real-time while the target application is running. On
the host platform, an RTDX host library operates in conjunction with Code Composer Studio
IDE. Data visualization and analysis tools communicate with RTDX through COM APIs to
obtain the target data and/or to send data to the DSP application. The host library supports
two modes of receiving data from a target application: continuous and non-continuous.
Code Composer

Studio CCS

MATLAB

Embedded
Target for
Texas
Instruments
DSP
+
Real Time
Workshop

Texas Instruments
DSP

Simulink
Model

Build and
Download

Application
+
DSP/BIOS
Kernel

RTDX

DSP/BIOS
Tools

RTDX

Fig.5.8. DSP BIOS and RTDX

In continuous mode, the data is simply buffered by the RTDX Host Library and is not
written to a log file. Continuous mode should be used when the developer wants to
continuously obtain and display the data from a target application and does not need to store
the data in a log file.
The realization of an interface is possible thanks to the Real-Time Data Exchange
(RTDX). RTDX allows transferring data between a host computer and target devices without
interfering with the target application. The data can be analyzed and visualized on the host
using the COM interface provided by RTDX. Clients such as Visual Basic, Visual C++,
Excel, LabView, MATLAB, and others are readily capable of utilizing the COM interface.

53

5.2 Code Composer Studio as Integrated Development Environment
Code Composer Studio is the DSP industry's first fully integrated development
environment (IDE) [50] with DSP-specific functionality. With a familiar environment like
MS-based C++TM; Code Composer lets you edit, build, debug, profile and manage projects
from a single unified environment. Other unique features include graphical signal analysis,
injection/extraction of data signals via file I/O, multi-processor debugging, automated testing
and customization via a C-interpretive scripting language and much more.

Fig.5.9. Code compose studio platform
Real-time analysis can be performed using real-time data exchange (RTDX). RTDX allows
for data exchange between the host PC and the target DSK, as well as analysis in real time without
stopping the target. Key statistics and performance can be monitored in real time. Through the joint
team action group (JTAG), communication with on-chip emulation support occurs to control and
monitor program execution. The C6713 DSK board includes a JTAG interface through the USB port.

Fig.5.10. Embedded software development

54

Source

Efficiency

Effort

Compiler
Optimizer

80‐100%

  Low

Linear
ASM

Assembly
Optimizer

95‐100%

  Med

ASM

Hand
Optimizer

100%

  High

C
C++

Fig.5.11. Typical 67xx efficiency vs. efforts level for different codes

The Code composer studio supports three file formats (.c/c++, .sa, .asm) for writing
codes. Fig.5.11 shows the efficiency vs. efforts level for three kinds of source codes. If we
write the code in linear assembly then ASM optimizer is required to convert linear assembly
file (.sa) to assembly file (.asm). Similarly if the code is written in C, the C compiler is
required to produce an assembly source file with extension .asm. The assembler assembles
.asm source file to produce a machine language object file with extension .obj. The linker
combines object files and object libraries as input to produce an executable file with
extension .out. This executable file represents a linked common object file format (COFF),
popular in Unix-based systems and adopted by several digital signal processor developers
[52]. This executable file can be loaded and run directly on the C6713 processor. Fig.5.12
and Fig.5.13 illustrate the process of target file generation.

.sa

ASM
Optimizer

Text
Editor

Link.cm

Assembler
.asm

Linker
.obj

.c/.cpp
.map

Compiler
Fig.5.12. Code generation

55

.out

C

    ASM
File

    C

Assembler

Compiler

Binary
File

Binary
File

Binary
File
Debugger

     Linker
Profiler

  Library
Exec.
File
Fig.5.13. Cross development environment

To create an application project, one can “add” the appropriate files to the project.
Compiler/linker options can readily be specified. A number of debugging features are
available, including setting breakpoints and watching variables, viewing memory, registers,
mixing C and assembly code, graphing results, and monitoring execution time. One can step
through a program in different ways (step into, over, or out). Fig. 5.14 shows the signal flow
during the processing.

Fig.5.14. Signal flow during processing

56

Code composer features include:
IDE with an editor, compiler, assembler, optimizer, debugger, etc.
‘C/C++’ compiler, assembly optimizes and linker.
Simulator.
Real-time operating system (DSP/BIOS™).
Real-Time Data Exchange (RTDX™) between the host and target.
Real-time analysis and data visualization.
Advanced watch windows.
Integrated editor.
File I/O, Probe Points, and graphical algorithm scope probes.
Advanced graphical signal analysis.
Visual project management system.
Multi-processor debugging.

Fig.5.15. Real-time analysis and data visualization

57

5.3 MATLAB interfacing with CCS and DSP Processor

Fig.5.16. MATLAB interfacing with CCS and DSP processor

Fig.5.16 depicts how the MATLAB is used as an interface for calling code composer
studio (CCS) and then the program is loaded into the TI instrument target. First of all
MATLAB code for the desired algorithm is written and then simulated for obtaining the
results in MATLAB graph window. However if we want that the code written for MATLAB
or the designed simulink model can be loaded in to the TI target then we can also perform
some real time results depending upon the used algorithm.

5.4 Real-time Experimental Setup using DSP Processor
The basic experimental setup for the hardware implementation of adaptive noise
canceller is depicted in Fig.5.17 and the real image of setup is shown in Fig.5.18. The input
signal can be provided to the DSP processor either through microphone or function generator
on MIC IN or LINE IN port respectively. The development software, Code Composer Studio
and simulation software MATLAB version 7.4 are installed on the PC and are used for
coding the algorithm and linking the coded algorithm to the target processor. The input signal
reaches to processor in digital form after the conversion by AIC23 onboard codec. The C
code is generated using real-time workshop available in MATLAB & Simulink and loaded on
the DSP processor. The input signal is processed according to code loaded into the processor
memory. For interactive feedback 4 DIP switches can be used. When the signal processing is

58

completed the output can be taken at HP OUT or LINE OUT port with the help of headphone
or CRO/DSO (refer Fig.5.17).

Fig.5.17. Experimental setup using Texas Instrument processor

Fig.5.18. Real-time experimental setup using DSP processor

The real time implementation can be done in the following manner: First of all, the
simulink model is developed (refer section 4.2) for NLMS algorithm and then connected to
the CCS by RTDX link to create a project in the CCS as shown in Fig.5.19 [47].

59

Fig.5.19. Model building using RTW

When the link get establish the CCS opens, the project is created automatically and
the process of code generation started as shown in Fig.5.20.

Fig.5.20. Code generation using RTDX link

60

After code generation the code is compiled and during the compilation process
compiler and debugger check the generated code for the errors. If there is any error code
compile operation gets fail and gives the information about the error. Further these errors can
be rectified and compilation process continues. When the compilation gets over the project is
rebuild to generate .out executable file which is to be loaded on the target processor. Once the
executable file is loaded in the processor memory, the processor is ready to use. Fig.5.21
shows the target processor in running position. Now the input can be applied to the processor
through line-in port using a function generator and output can be taken from line-out port
using DSO as shown in Fig.5.18.

Fig.5.21. Target processor in running status

If we investigate the simulink model (refer Fig.4.2), a DIP switch is used to control
the flow of output signal and is configured as:
When switch position is 0: The input of processor is directed toward output without
filtering. The DIP switch at ‘Zero’ position is shown in Fig.5.22 (a).When Switch Position is
1: The NLMS filter start working and the output is the filtered version of input. The DIP
switch at ‘one’ position is shown in Fig.5.22 (b).

61

Fig.5.22 (a) Switch at Position 0

Fig.5.22 (b) Switch at position 1 for NLMS noise reduction

In this chapter an introduction of TMS320C6713 DSK hardware with features was
presented. Then a brief introduction of the software environment CCStudio that used to build
the project and create executable file for the DSP processor was also discussed.
A model which was designed in previous chapter using simulink is connected to the
DSP processor with the Real-Time Workshop (RTW) and the code is generated. The
generated code is downloaded from host to target processor using RTDX link and run on
processor. The output results are presented and discussed next in the chapter-6.

62

Chapter-6

RESULTS AND DISCUSSION
In this chapter MATLAB simulation and real-time hardware implementation results
for adaptive noise cancellation system are presented. The results are arranged in two sections;
first section deals with the MATLAB simulation of LMS, NLMS and RLS adaptive filter
algorithms when tone signal is applied as an input signal. A fair performance comparison of
simulation results for all three algorithms is also presented in terms of mean squared error,
computational complexity, percentage noise removal and stability. The next section shows
the hardware implementation results for NLMS & LMS algorithms when implemented on
TMS320C6713 DSP processor. Primarily the filtering is done for a tone signal. The effect of
frequency and amplitude variation of a tone signal on the filter performance is also
investigated. Further the filtering is done when an ECG signal is taken as an input to make
the designed system more practical and implementable. Finally a SNR improvement
comparison for NLMS and LMS algorithms is presented when ECG is taken as input signal
and implemented on DSK hardware.

6.1

MATLAB Simulation Results for Adaptive Algorithms
In the MATLAB simulation the reference input signal x(n) is a white Gaussian noise

of power 2-dB generated using randn function, s(n) is a clean sinusoidal tone signal of
amplitude 2V. The desired signal d(n) obtained by adding a delayed version of x(n) into clean
signal s(n), d(n) = s(n) + x1(n) as shown in Fig.6.1.

Fig.6.1. (a) Clean tone (sinusoid) signal s(n),(b)Noise signal x(n)

63

Fig.6.1. (c) Delayed noise signal x1(n), (d) desired signal d(n)

6.1.1 LMS Algorithm Simulation Results
The simulation of the LMS algorithm is carried out with the following specifications:
Filter order N=19, step size µ= 0.001, and iterations= 8000.

Fig.6.2. MATLAB simulation for LMS algorithm; N=19, step size=0.001

The LMS algorithm is simple and easy to implement but the convergence speed is
slow, it can be seen from the simulation results derived in Fig.6.2. The LMS based filter
adopts the approximate correct output in 2800 samples as shown in Fig.6.2 (a), the
corresponding mean squared error generated as per adaption of filter parameters is shown in
Fig.6.2 (b). The average Mean Squared Error (MSE) achieved for LMS algorithm is
2.5×10-2. The value of MSE for LMS algorithm highly depends on the step size µ. This is
illustrated in Fig 6.3, which is derived by the simulation of LMS algorithm at different values
of step size, varied from 0.0001 to 0.01. The corresponding numeric data for the Fig.6.3 is
presented in Table 6.1.

64

TABLE 6.1
MEAN SQUARED ERROR (MSE) VERSUS S TEP SIZE (µ)

S.N.

Step-size(µ)

Mean Squared
Error(MSE)

1.

0.0001

0.1281

2.

0.0002

0.0738

3.

0.0003

0.0516

4.

0.0004

0.0404

5.

0.0005

0.0340

6.

0.0006

0.0300

7.

0.0007

0.0275

8.

0.0008

0.0259

9.

0.0009

0.0249

10.

0.001

0.0244

11.

0.002

0.0308

12.

0.003

.0448

13.

0.004

0.0618

14.

0.005

0.0805

15.

0.006

0.1005

16.

0.007

0.1215

17.

0.008

0.1437

18.

0.009

0.1671

19.

0.01

0.1918

65

Fig.6.3. MSE versus step-size (µ) for LMS algorithm

From Table 6.1 and Fig.6.3 it is clear that when the value of µ is too small (0.0001)
the mean squared error is too large (0.1281). As we increase the step-size, the mean squared
error gets reduced but after a limit (µ=0.001) the mean squared error starts increasing as we
increase the step-size (µ>0.001). Hence the selection of the proper value of step-size for
specific application is prominent in getting good results.

6.1.2 NLMS Algorithm Simulation Results
The simulation of the NLMS algorithm is also carried out with the same parameters as
for LMS algorithm: Filter order N=19, step size µ= 0.001 and iterations= 8000.
In case of NLMS algorithm step size is not fixed, it varies at each iteration on the
basis of the input signal energy. Therefore the filter performance improves and less time is
required as compared to LMS algorithm to converge on the optimum solution. The NLMS
based filter adopt the approximate correct output in 2300 samples as shown in Fig.6.4 (a),
the corresponding mean squared error generated as per adaption of filter parameters is shown
in Fig.6.4 (b). The average MSE achieved for NLMS algorithm is 2.1×10-2.

66

Fig.6.4. MATLAB simulation for NLMS algorithm; N=19, step size=0.001

6.1.3 RLS Algorithm Simulation Results
The simulation of the RLS algorithm is carried out with the following specifications:
Filter order N=19, iterations= 8000, and a positive constant λ=1.

Fig.6.5. MATLAB simulation for RLS algorithm; N=19, λ=1

The RLS algorithm is much faster and produces a minimum mean squared error , it
can be seen in Fig.6.5. The RLS based filter adopt the approximate correct output in 300
samples as shown in Fig.6.5 (a), the corresponding mean squared error generated as per
adaption of filter parameters is shown in Fig.6.5 (b). The average MSE achieved for RLS
algorithm is 1.7×10-2.

6.1.4 Performance Comparison of Adaptive Algorithms
If we compare the filtered output and mean squared error of all algorithms(refer
Fig.6.2,Fig.6.4, Fig.6.5), LMS adopt the approximate correct output in 2800 samples with an
average MSE of 2.5×10-2, NLMS adopt in 2300 samples with an average MSE of 2.1×10-2
and RLS adopt in 300 samples with an average MSE of 1.7×10-2. This shows that RLS has

67

faster learning rate with least MSE. But in practical applications the implementation of RLS
algorithm is limited due to the larger computational complexity and memory requirements.
The filter order also affects the performance of a noise cancellation system. Fig.6.6
illustrates how the MSE changes as we change filter order. When filter order is less (<15),
LMS has good MSE as compared to NLMS and RLS but as the filter order increases (>15)
the performance of RLS becomes better and LMS has poor performance. It justifies the fact
that the selection of right filter order is necessary to achieve the best performance. In this
work the appropriate filter order is 19 therefore all simulations are carried out at N=19.

Fig.6.6. MSE versus filter order (N)

For proper filtering filter order should be higher but as we increase the filter order the
convergence speed of the filter get slower, therefore a proper selection of filter order and
suitable adaptive algorithm is imperative to the performance of the system. Table 6.2
illustrates the performance comparison of LMS, NLMS and RLS algorithms in terms of MSE
when filter order is changed.

68

TABLE 6.2
MEAN SQUARED ERROR (MSE) VERSUS FILTER-ORDER (N)

S.N
1.
2.
3.

Filter-order(N)
1
2
3

MSE (LMS)
0.3044
0.3061
0.3075

MSE(NLMS)
0.6092
0.4261
0.3699

MSE(RLS)
0.3059
0.3123
0.3121

4.
5.
6.
7.

4
5
6
7

0.3088
0.3098
0.3104
0.3113

0.3487
0.3408
0.3380
0.3352

0.3082
0.3059
0.2977
0.3121

8.
9.
10.
11.

8
9
10
11

0.3127
0.3135
0.3143
0.3142

0.3330
0.3305
0.3280
0.3250

0.3103
0.3109
0.3139
0.3249

12.
13.
14.
15.

12
13
14
15

0.3146
0.3094
0.3105
0.2508

0.3227
0.3155
0.3146
0.2524

0.3032
0.3394
0.3207
0.2448

16.
17.
18.
19.

16
17
18
19

0.1001
0.0408
0.0421
0.0374

0.0995
0.0388
0.0394
0.0344

0.0914
0.0390
0.0254
0.0188

20.
21.
22.
23.

20
21
22
23

0.0384
0.0382
0.0394
0.0401

0.0349
0.0344
0.0355
0.0358

0.0214
0.0278
0.0312
0.0264

24.
25.
26.
27.

24
25
26
27

0.0411
0.0420
0.0430
0.0441

0.0363
0.0367
0.0373
0.0380

0.0232
0.0400
0.0440
0.0468

28.
29.
30.
31.

28
29
30
31

0.0452
0.0463
0.0473
0.0483

0.0388
0.0397
0.0405
0.0412

0.0407
0.0531
0.0342
0.0344

32.
33.

32
33

0.0492
0.0501

0.0418
0.0425

0.0469
0.0476

69

S.N
34.
35.
36.

Filter-order(N)
34
35
36

MSE (LMS)
0.0509
0.0519
0.0529

MSE(NLMS)
0.0435
0.0446
0.0456

MSE(RLS)
0.0500
0.0542
0.0577

37.
38.
39.
40.

37
38
39
40

0.0539
0.0547
0.0555
0.0563

0.0464
0.0469
0.0476
0.0484

0.0594
0.0604
0.0663
0.0777

41.
42.
43.
44.

41
42
43
44

0.0571
0.0580
0.0589
0.0598

0.0493
0.0501
0.0510
0.0518

0.0953
0.1142
0.1185
0.1231

45.

45

0.0606

0.0525

0.1350

TABLE 6.3
PERFORMANCE COMPARISON OF VARIOUS ADAPTIVE ALGORITHMS

S.N

Algorithm

MSE

1.

LMS

2.
3.

% Noise
Reduction

Complexity (No. of
multiplications per

Stability

2.5×10-2

91.62%

2N+1

Highly Stable

-2

93.85%

3N+1

Stable

2.1×10

NLMS

-2

1.7×10

RLS

98.78%

4N

2

less Stable

TABLE 6.4
COMPARISON OF VARIOUS PARAMETERS FOR ADAPTIVE ALGORITHMS

Algorithm

LMS

NLMS

RLS

Convergence Time

Very slow

Slow

Fast

Complexity

Very Simple

Simple

High

MIPS consumption

Very Low

Low

High

Implementation

Very Simple

Simple

Complex

Parameters

70

Table 6.3 and Table 6.4 represent the performance analysis of adaptive filter
algorithms. In Table 6.3 performance analysis of all three algorithms is presented in term of
MSE, percentage noise reduction, computational complexity and stability. It is clear from the
Table 6.3 that computational complexity and stability problems increases in an algorithm as
we try to reduce the mean squared error. The LMS algorithm has 2N+1 number of
multiplications at each iteration with 91.62% noise reduction. The NLMS algorithm has
3N+1 number of multiplications at each iteration with 93.85% noise reduction. The RLS
algorithm has 4N2 number of multiplications at each iteration with 98.78% noise reduction.
These results shows that the noise reduction in RLS algorithm is highest but at the
same time computational complexity is also higher and also encounters stability problems
sometimes. NLMS algorithm has only N number of additional multiplications as compared
to LMS algorithm for better filtering and is stable, less complex as compared to RLS
algorithm. Therefore, NLMS is the favorable choice for most of the industries and practical
applications.

6.2

Hardware Implementation Results using TMS320C6713 Processor
The experimental setup for real-time noise cancellation is depicted in Chapter 5

(Fig.5.18). The model is created in simulink and is connected to the TMS320C6713 processor
using real-time workshop (refer Fig.5.19). The model is tested with two types of signals viz.
tone signal and ECG signal. The output results are measured with the help of DSO.

6.2.1 Tone Signal Analysis using NLMS Algorithm
In this section real-time results of DSP Processor for a tone (sinusoidal) signal are
presented. Initially a clean tone-signal of 2-dB power and 1 kHz frequency as shown in
Fig.6.7 is generated using function generator and then random noise is added to it with the
help of noise generator so the signal becomes a noisy signal as illustrated in Fig. 6.8.This
noisy signal is applied at the “Line In” port of DSK, which is processed as per the program
running on the DSK and the filtered output is taken from “Line Out” port of the processor kit.
A MATLAB program is written to calculate the SNR of the noisy signal and filtered
signal. The filtered output in Fig.6.9 shows a considerable improvement in the signal quality
with an average SNR improvement of 11dB.

71

Fig.6.7. Clean tone signal of 1 kHz

Fig.6.8. Noise corrupted tone signal

Fig. 6.10 illustrates the time delay introduced by hardware components where the
filtered output is delayed by a period of 0.4ms. The delay time between the desired signal and
the filtered signal is very short which enables the noise-cancellation in real-time. Although
the power of filtered signal is reduced but the accuracy in filtered signal is excellent. The
reduced power of the filtered signal can be amplified by the amplifier as per the requirement
of the application.

72

Fig.6.9. Filtered tone signal

Fig.6.10. Time delay in filtered signal

6.2.1.1 Effect on Filter Performance at Various Frequencies

Investigations are carried out for the tone signals at various frequencies. When we
increase the signal frequency the voltage level gets reduced which has to be maintained at
certain level. Here the voltage level is kept at 2V for the sake of experimentation and the
frequencies are varied from 2 kHz to 5 kHz. The effect of frequency variations on the filter
performance can be visualized in the Fig. 6.11.

73

Fig.6.11. (a) Filtered output signal at 2 kHz frequency

Fig.6.11. (b) Filtered output signal at 3 kHz frequency

Fig. 6.11 illustrates how the noisy signal and its filtering gets affected as we increase
the frequency of the clean signal. When we increase the frequency, the noise component in
desired signal gets increased or decreased as per the frequency correlation of noise and clean
signal. When the noise lies in the same frequency band of clean signal, signal gets more noisy
and results in poor filtering as shown in Fig.6.11 (d), When the frequency of noise and clean
signal is not matched, the desired signal is less affected by the noise and results in fine
filtering as illustrated in Fig. 6.11 (a), Fig.6.11 (b) & Fig. 6.11 (c).

74

Fig.6.11. (c) Filtered output signal at 4 kHz frequency

Fig.6.11. (d) Filtered output signal at 5 kHz frequency

6.2.1.2 Effect on Filter Performance at Various Amplitudes

Now some other kinds of measurements are taken to check effect of noise on the
filtered signal when the amplitude of clean signal is varied. The tone signal frequency is fixed
at 1 kHz and the amplitude of tone signal is varied from 3V to 5V.

75

Fig.6.12. (a) Filtered output signal at 3V

Fig.6.12. (b) Filtered output signal at 4V

When the amplitude of clean tone signal is increased the comparative amplitude of
noise get reduced which marginally effects the clean signal and results in a higher degree of
SNR improvement up to 13dB. Fig. 6.12 shows the corresponding waveforms.

76

Fig.6.12. (c) Filtered output signal at 5V

Fig.6.13. Filtered signal at high noise

The investigation so far carried out for tone signal was based on low or medium noise
environments where the obtained result shows a reasonable level of SNR improvement.
Fig.6.13 shows the system consistency in high level noise environment by making an average
SNR improvement of 10dB for filtered signal. A tabular presentation of SNR improvement
versus frequency & amplitude variations is presented in Table 6.5 and SNR Improvement
versus Noise Level is presented in Table 6.6.

77

TABLE 6.5
SNR IMPROVEMENT VERSUS VOLTAGE AND FREQUENCY

S.N.

Amplitude
(V)

Frequency
(kHz)

SNR Improvement
(dB)

1.

2

1

11.00

2.

3

1

11.52

3.

4

1

11.93

4.

5

1

12.80

5.

2

2

11.58

6.

2

3

11.93

7.

2

4

12.08

8.

2

5

11.66

TABLE 6.6
SNR IMPROVEMENT VERSUS NOISE LEVEL FOR A TONE SIGNAL

S.N. Noise Level

Noise Variance

SNR Improvement
(dB)

1.

Low

0.02

13

2.

Medium

0.05

12

3.

High

0.15

10

6.2.2 ECG Signal Analysis using NLMS and LMS Algorithms and their
Performance Comparison
The ECG or the electrocardiogram is a biomedical signal. It is the electrical
manifestation of the contractile activity of the heart. ECG is a quasi- periodical, rhythmically
repeating signal, synchronized by the function of the heart which acts as the generator of
bioelectrical events. A typical ECG cycle is defined by the various features (P, Q, R, S, and
T) of the electrical wave.

78

Fig.6.14. ECG waveform

The P wave marks the activation of the atria, which are the chambers of the heart that
receive blood from the body. The activation of the left atrium which collects oxygen-rich
blood from the lungs and the right atrium which gathers oxygen-deficient blood from the
body takes about 90 msec. Next in the ECG cycle comes the QRS complex. The heart beat
cycle is measured as the time between the second of the three parts of the QRS complex, the
large R peak. The QRS complex represents the activation of the left ventricle which sends
oxygen-rich blood to the body, and the right ventricle which sends oxygen-deficient blood to
the lungs. During the QRS complex, which lasts about 80 msec, the atria prepare for the next
beat, and the ventricles relax in the long T wave. These are the features of the ECG signal by
which a cardiologist uses to analyze the health of the heart and note various disorders, such as
atrial flutter, fibrillation, and bundle branch blocks.
The ECG signal is a very weak time varying signal (about 0.5mV) and has a
frequency between 0.5Hz to 100Hz. Therefore it is more prone to interference from the
environmental noise. Thus the waveforms recorded have been standardized in terms of
amplitude and phase relationships and any deviation from this would reflect the presence of
an abnormality. Abnormal patterns of ECG may be due to undesirable artifacts, Normally
ECG is contaminated by power-line interference of 50Hz. So it is desired to eliminate this
noise and to find how best the signal can be improved.

79

In this section, an attempt is made to denoise an ECG signal with the help of Least
Mean Square based adaptive filters implemented on TMS320C6713 DSP processor in realtime environment. Then a performance comparison of NLMS & LMS algorithms based on
average SNR improvement is presented for a real-time biomedical signal.
Fig.6.15 shows a clean (amplified) ECG signal with 1000 sample values of amplitude
260mV and frequency 35 Hz generated through twelve lead configurations, sampled at a
frequency of 1.5 kHz.

Fig.6.15. Clean ECG signal

The NLMS & LMS based designed adaptive filter models are tested for three levels
(low, medium and high) of noise corrupted ECG signals. The samples of noisy and filtered
ECG signals are stored in a comma separated value (.csv) file with the help of DSO. This
(.csv) file is used in a MATLAB program to calculate SNR before filtering and after filtering,
which gives an estimate of an average SNR improvement in the filtered signal.
If we analyse the filtered output of low noise ECG signal (Fig.6.16), we find that there
is a high degree of filtering with an average SNR improvement of 9.89 dB for NLMS and
8.85 dB for LMS algorithms. This shows that the filtered signal is approximately equal to the
clean signal.

80

Fig.6.16. (a) NLMS filtered output for low level noisy ECG signal

Fig.6.16. (b) LMS filtered output for low level noisy ECG signal

In the second case (refer Fig.6.17), when medium level of noise contaminates the
signal, the average SNR improvements in filtered signals are 8.62 dB and 7.55 dB for NLMS
& LMS algorithms respectively. The last case (refer Fig.6.18) deals with high level of noisy
environment where due to noise, the peaks of R wave matches with the peaks of T wave
which makes it difficult to measure the heart rate of a patient because heart rate is measured
with help of peaks of QRS complex.

81

Fig.6.17. (a) NLMS filtered output for medium level noisy ECG signal

Fig.6.17. (b) LMS filtered output for medium level noisy ECG signal

The problem is solved in the filtered signal (Fig.6.18) which preserves the peaks of
each QRS complex and cuts down the peak of noisy T waves with an average SNR
improvement of 6.38 dB & 5.12 dB for NLMS & LMS algorithm respectively.

82

Fig.6.18. (a) NLMS filtered output for high level noisy ECG signal

Fig.6.18. (b) LMS filtered output for high level noisy ECG signal

In Table 6.7, an analysis of SNR Improvement is presented with respect to the noise
variance for NLMS filtered and LMS filtered waves. It is clear from the Table 6.7, the
performance of NLMS algorithm based filter is much better than LMS based filter with an
average SNR difference upto 1.26 dB.

83

TABLE 6.7
SNR IMPROVEMENT VERSUS NOISE VARIANCE FOR AN ECG S IGNAL

S.N.

Noise
Variance

Sampling Rate
(kHz)

SNR Improvement
NLMS (dB)

SNR Improvement
LMS (dB)

1.

0.02

1.5

9.89

8.85

2.

0.05

1.5

8.62

7.55

3.

0.1

1.5

6.38

5.12

The above results justify that the proposed real-time hardware implementation of
NLMS algorithm shows a considerable improvement in the SNR of a noisy signal and the
performance of the proposed system is better than the available LMS based systems. The
hardware implementation of NLMS algorithm enables one to work with real-time biomedical
and other kind of signals whereas simulation does not provide real-time working
environment. The background noise for tone and ECG signals were eliminated adequately
with reasonable rate for all the tested noises. When system is tested with tone signal in low
and medium power noises, the system showed SNR improvement upto 13 dB and in high
power noise environment SNR improvement is of 10 dB. When the measurements are carried
out with a biomedical ECG signal, the SNR improvement is achieved upto 9.89 dB at low,
8.62 dB at medium noise and 6.38 dB for high noise environment. The filtered output
preserves all the parameters of biomedical signal which are used for diagnosis purpose.
Therefore based on these results, the designed system proves to be successful in the removal
of noise form a desired signal such as ECG signal or any other type of biomedical diagnostic
signal.

84

Chapter-7

CONCLUSIONS
7.1

Conclusion
In the present work three adaptive filter algorithms; LMS, NLMS & RLS are

implemented on MATLAB and the simulation results are analyzed for a tone signal. A fair
performance comparison has been presented among the discussed algorithms based on the
popular performance indices like Mean Squared Error (MSE), convergence speed,
computational complexity etc.
The simulation results show that the LMS algorithm has slow convergence, high MSE
(2.5×10-2) but it is simple to implement and gives good results if step size is chosen correctly.
The RLS algorithm has the highest convergence speed, less MSE (1.7×10-2) but at the cost of
large computational complexity and memory requirement that makes it difficult to realize on
the hardware. In case of NLMS algorithm, the MSE is 2.1×10-2, hence its performance lies
between LMS and RLS algorithms. Therefore it provides a trade-off in convergence speed
and computational complexity.
The NLMS and LMS algorithms are then implemented on the TMS320C6713
processor for real-time noise cancellation. The filter performance is measured in terms of
SNR improvement. The results were analyzed for two types of signals; tone signal and ECG
signal with the help of DSO. The tone signal has been analyzed at various frequencies and
voltage level to check the effect of noise on the filtering. We find that the effect of noise gets
more prominent when the frequency of noise and clean signal is highly correlated or noise
signal has higher amplitude.
The designed system is further tested for three ECG signals of different noise level for
NLMS algorithm and LMS algorithm. A fair amount of SNR improvement (upto 9.89 dB and
8.85 dB respectively) is achieved in both algorithms and the filtered ECG signal was found
useful for medical diagnosis purposes. When the results of two algorithms were compared, it
is found that the NLMS algorithm has shown better performance with the advancement of
1.26 dB in the average SNR improvement.

85

7.2

Future Scope
Considering the nature of the experiment, there are a number of viable directions for

the extension of the research. An interesting extension would be implementing different kind
of adaptive filter algorithms like Time Varying LMS (TVLMS), Variable Step Size NLMS
(VSSNLMS), Fast Transversal RLS (FTRLS) etc. that may perform with faster convergence
and better noise reduction.
Another useful extension of this thesis would be in the use of larger number of filter
coefficients. Depending on the application, many of the adaptive filters in practice use a large
number of filter coefficients. This is necessary when the time delay spread of a system is
large requiring long filters as in the case of noise cancellation. It is common to find the filters
of order 2048 or larger. In such applications, the convergence speed is significantly slower
than it is for the shorter filter lengths. Therefore, in those cases the convergence speed and the
ways to improve performance becomes a critical factor. Performing this experiment,
however, requires redesigning the current hardware platform enabling the use of more
powerful processor that could handle the extended computational load.
There are many other possibilities for further development in this discipline. Some of
them are as follows:
The

noise

cancellation

system

was

implemented

successfully

using

the

TMS320C6713 DSK. However, the system was implemented using auto C code
generation which takes more memory on the board which limits the hardware
performance. Coding in assembler could allow for further optimization and an
improvement in the systems performance.
The implemented noise cancellation system is mainly analysed for tone signals and
ECG signals. However someone can also analyse it for other kind of noise corrupted
signals.
The noise cancellation system was developed on the DSK board. This has certain
parameters such as sampling rate that are unalterable by the developer. Another
possible way to increase the performance of the noise cancellation system is to use the

86

C6713 digital signal processor in a custom made circuit which can properly utilize its
full potential.
This thesis deals with transversal FIR adaptive filters; this is only one of many
methods of digital filtering. Other techniques such as infinite impulse response (IIR)
or lattice filtering may prove to be more effective in an adaptive noise reduction
application but ask for enough memory requirements.
The algorithms studied in this thesis perform best under purely stationary signal
conditions. Further work could be done in developing techniques specifically
designed for non-stationary signals.
For different applications, different characteristics and performance measures are
important. Wavelet transforms can give advantages and disadvantages in different
aspects of the application. Such an experiment could be done on the same or similar
hardware as the one used in this experiment.
I feel that the goals of this thesis have been accomplished. But, the field of digital
signal processing and in particular adaptive filtering is vast and further research and
development in this discipline can only lead to an improvement on the methods for Adaptive
noise cancellation systems studied in this dissertation.

87

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92

APPENDIX-I

LIST OF PUBLICATIONS
International/ National Journals (Published/Accepted)
[1] Raj kumar Thenua and S.K. Agarwal, “Simulation and Performance Analysis of
Adaptive Filter in Noise Cancellation”, International Journal of Engineering Science
and Technology (IJEST), ISSN: 0975-5462, Vol. 2(9), 2010, Page no. 4374-4379.
(Published)

International/ National Conferences (Published/Accepted)
[2] Raj kumar Thenua and S.K. Agarwal, “Hardware Implementation of Adaptive
algorithms for Noise Cancellation”, IEEE International Conference on Network
Communication and Computer (ICNCC 2011), 21st -23rd Mar 2011, organized by
International Association of Computer Science and Information Technology (IACSIT)
and Singapore Institute of Electronics (SIE) at New Delhi, India. (Published)
[3] Raj kumar Thenua, S.K. Agarwal and Mohd. Ayub khan, “Performance analyses of
Adaptive Noise Canceller for an ECG signal” International Conference on Recent
Trends in Engineering, Technology and Management on 26th -27th Feb 2011 at BIET,
Jhansi, India. (Published)
[4] Raj kumar Thenua and S.K. Agarwal, “Hardware Implementation of NLMS
Algorithm for Adaptive Noise Cancellation”, National Conference on Electronics and
Communication (NCEC-2010) on 22nd -24th December 2010 at MITS, Gwalior.
(Published)
[5] Raj kumar Thenua and S.K. Agarwal, “Real-time Noise Cancellation using Digital
Signal Processor”, National conference on Electronics, Computers and
Communications (NCECC-2010) on 06th -07th March 2010 at MITS, Gwalior.
(Published)

93

APPENDIX-II

MATLAB COMMANDS
load

Load workspace variables from disk

randn

Normally distributed random numbers

fir1

Window-based finite impulse response filter design

filter

1-D digital filter

zeros

Create array of all zeros

dot

Vector dot product

mean

Average or mean value of array

sum

Sum of array elements

abs

Absolute value and complex magnitude

eye

Identity matrix

hold

Retain current graph in figure

disp

Display text or array

simulink

Open Simulink block library

wavwrite

Writes data to 8-, 16-, 24-, and 32-bit .wav files

csvread

Read comma-separated value file

ccsboardinfo

Information about boards and simulators known to CCS IDE

ccsdsp

Create link to CCS IDE

enable

Enable RTDX interface, specified channel, or all RTDX
channels

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M.Tech Thesis on Simulation and Hardware Implementation of NLMS algorithm on TMS320C6713 Digital Signal Processor

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