Analysis of different FIR Filter Design Method in terms of Resource Utilization and Response on Field-Programmable Gate Array
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This paper presents an analysis of fully parallel FIR filter designs implemented on FPGA, comparing three design methods: equiripple, least-squares, and least pth-norm. Results indicate that the equiripple design outperforms the other methods in resource utilization and response performance. The study emphasizes the importance of optimizing digital filters for efficiency in high-speed applications, particularly in modern communication systems.
![IJSRD - International Journal for Scientific Research & Development| Vol. 1, Issue 5, 2013 | ISSN (online): 2321-0613
All rights reserved by www.ijsrd.com 1093
Abstract--In this paper fully parallel FIR filters are designed
with different design method on FPGA for resource
utilization and response analysis. fully parallel band-pass
FIR filters with same specification designed and simulated
on ISE. The suggested implementations are synthesized with
Xilinx ISE 14.2 version. Results show comparison of three
different filter design methods in terms of resource
utilization.
I. INTRODUCTION
Digital filters are important part of digital signal processing.
Before development of FPGA digital filter were
implemented on digital signal processor. Digital signal
processors are still widely used but they are not capable for
high speed application available in present. After the
advancement of microelectronic techniques, communication
signal processing has come to third generation and forth
generation period, so there is a challenge for adaptive
processing techniques that the processing speed needs to be
high so FPGA based signal processing techniques is mostly
used in latest mobile communication, military
communication, consumer electronics and aerospace
tracking etc so that It is necessary to find the answer of how
to increase operation speed of signal processing algorithms
and reduce hardware resources by adopting FPGA to
implement every kinds of tasks of digital signal processing.
So we look forward for design of digital filter with low area
and high speed. Benefits of reducing area:
(a) Less power required
(b) Area benefits for other application on same chip
(c) We can use versions of FPGA which have less
capability.
Digital filters are typically used to modify or alter
the attributes of a signal in the time or frequency domain.
The most common digital filter is the linear time-invariant
(LTI) filter. An LTI interacts with its input signal through a
process called linear convolution, denoted by y = f * x
where f is the filter's impulse response, x is the input signal,
and y is the convolved output. The linear convolution
process is [1] formally defined by:
y[n] = x[n] * f[n] = ∑ [ ] [ ]
= ∑ [ ] [ ] (1)[1]
LTI digital filters are generally classified as being finite
impulse response (i.e., FIR), or infinite impulse response
(i.e., IIR). Calculating the constant coefficients of such a
digital filter involves considerable amount of computation
and this is generally performed using software tools [1].
With available digital filter design software the
production of FIR coefficients is a straightforward process.
The Filter Design and Analysis (FDA) tool packaged along
with MATLAB is such a tool. The double length floating
point notation for filter coefficients, used by the FDA tool
poses immense challenges in terms of cost and resources,
while implementing on an FPGA [1].
The challenge remains is to map the FIR design
into a suitable architecture. To overcome this, the filter
coefficients have to be quantized to a fixed point notation.
The result of coefficient quantization is that the actual
implemented transfer function is different from the ideal
transfer function. The simplest and most widely used
approach to the problem is to round off the optimal infinite
precision coefficients to a b-bit representation [1].
II. PARALLEL AND SERIAL ARCHITECTURES
The basic equation for a single-channel FIR filter is shown
in equation [1]
( ) ∑ ( ) ( ) (2)
The terms in the equation can be described as input samples,
output samples, and coefficients. Imagine x(n) as a
continuous stream of input samples and y(n) as a resulting
stream (i.e., a filtered stream) of output samples[1].
The n and k in the equation correspond to a
particular instant in time, so to compute the output sample
y(n) at time n, a group of input samples at N different points
in time, or x(n), x(n-1), x(n-2), ... x(n-N+ 1) is required[1].
The group of N input samples are multiplied by N
coefficients and summed together to form the final result
y(n).Fig. 1 shows the logical structure of an FIR Filter[1].
Fig. 1: Logical Structure of an FIR filter [1]
A fully parallel architecture uses a dedicated multiplier and
adder for each filter tap; all taps execute in parallel, thereby
creating fully parallel implementation. This architecture is
optimal for speed. However, it requires more multipliers and
adders than a serial architecture, and therefore consumes
more chip area. Fig. 2 shows the fully parallel architecture
of 64 tap FIR Filter [1].
Analysis of different FIR Filter Design Method in terms of Resource
Utilization and Response on Field-Programmable Gate Array
Nilesh B. Bosmiya1
Prof. R. C. Patel2
1
PG Student 2
Professor
1, 2
Dept. of Instrumentation & Control, L. D. College of Eng. Gujarat, India](https://image.slidesharecdn.com/ijsrdv1i5014-140805035405-phpapp01/85/Analysis-of-different-FIR-Filter-Design-Method-in-terms-of-Resource-Utilization-and-Response-on-Field-Programmable-Gate-Array-1-320.jpg)
![Analysis of different FIR Filter Design Method in terms of Resource Utilization and Response on Field-Programmable Gate Array
(IJSRD/Vol. 1/Issue 5/2013/0014)
All rights reserved by www.ijsrd.com 1094
Fig. 2: Parallel implementation of FIR filter [1]
III. FPGA SIMULATION AND RESULT COMPARISON
An FIR Band Pass filter is designed as per the specifications
given in table 1. With three different design method which
are Equiripple, Least-Squares, Least Pth-norm.
A special class of FIR filter that is particularly effective in
meeting
Frequency Value
Sampling Frequency 48000Hz
Stop band Frequency1 7250Hz
Pass band Frequency1 9650Hz
Pass band Frequency2 12050Hz
Stop band Frequency2 14450Hz
Stop band Attenuation1 80 dB
Pass band Attenuation 1 dB
Stop band Attenuation2 80 dB
Table. 1: Filter Specifications
Fig. 3: Response for reference filter with Equiripple design
Fig. 4: Response of the filter with Least-Squares design
Such specifications are called the equiripple FIR filter. An
equiripple design protocol minimizes the maximal
deviations (ripple error) from the ideal transfer function. The
filer designed for the mentioned specifications using
equiripple design method is of order 64[1].
Fig. 3 is for the response of the filter with Equiripple design.
Fig. 4 is for the response of the filter with Least-Squares
design. Fig. 5 is for the response of the filter with Least Pth
Norm design.
Fully parallel and filter was designed and its behavioural
simulation was done using Xilinx ISE 14.2. Resource
utilization for different filter design method is shown in
table 2.
Fig. 5: response of the filter with Least Pth-Norm design](https://image.slidesharecdn.com/ijsrdv1i5014-140805035405-phpapp01/85/Analysis-of-different-FIR-Filter-Design-Method-in-terms-of-Resource-Utilization-and-Response-on-Field-Programmable-Gate-Array-2-320.jpg)
![Analysis of different FIR Filter Design Method in terms of Resource Utilization and Response on Field-Programmable Gate Array
(IJSRD/Vol. 1/Issue 5/2013/0014)
All rights reserved by www.ijsrd.com 1095
Fig. 6: Waveform screenshot of software simulation for
fully parallel design
Equiripple
Least-
Squares
Least Pth-
Norm
Quantization Q16.14 Q16.14 Q16.14
Slices 2651 2797 2798
Slice Flip
Flops
1055 1055 1055
LUTs 4065 4358 4328
Max .Freq.
(MHz)
7.378MHz 7.373MHz 7.548MHz
Table. 2: Resource utilization for different filter design
method
Now the Starting portion of simulation result is shown in
Fig. 6.
IV. CONCLUSION
We can clearly see that from table II and response figures
equiripple design is superior than other two methods.
ACKNOWLEDGEMENTS
Author thanks Prof. R. C. Patel for his valuable guidance for
this paper. Author is also thankful to his staff and colleagues
for their co-operation.
REFERENCES
[1] V. Sudhakar, N. S .Murthy, L. Anjaneyulu, “fully
parallel and fully serial architecture for realization of
high speed FIR filters with FPGA’s Devices, Circuits
and Systems (ICDCS)” , 2012 International Conference
on Digital Object Identifier:
10.1109/ICDCSyst.2012.6188766 Publication Year:
2012, Page(s): 499 - 501 IEEE Conference
Publications.
[2] Vinger K. and Torresen J, "Implementing Evolution of
FIR filters efficiently in an FPGA", Proc. of2003
NASA/DoD Conference on Evolvable Hardware (EH-
2003), July, 2003, Chicago, Illinois, USA
[3] Shanthala S, and S. Y. Kulkarni, "High Speed and Low
Power FPGA Implementation of FIR Filter for DSP
Applications" European Journal of Scientific Research,
2009.
[4] Wonyong Sung and Ki-Il Kum, "Simulation Based
Word-Length Optimization Method for Fixed-point
Digital Signal Processing Systems", IEEE Transactions
on Signal Processing,Vo. 43, No.12, December 1995.
[5] X. Hu, L. S. DeBrunner, and V. DeBrunner, "An
efficient design for FIR filters with Variable precision",
Proc. 2002 IEEE Int. Symp. On Circuits And System.
[6] S. K. Mitra, “Digital Signal Processing: A computer-
Based Approach ”, 2nd
ed. McGraw-Hill, 1997.
[7] U. Meyer-Baese, “Digital Signal Processing with Field
Programmable Gate Arrays”, Springer, 2004.](https://image.slidesharecdn.com/ijsrdv1i5014-140805035405-phpapp01/85/Analysis-of-different-FIR-Filter-Design-Method-in-terms-of-Resource-Utilization-and-Response-on-Field-Programmable-Gate-Array-3-320.jpg)
Analysis of different FIR Filter Design Method in terms of Resource Utilization and Response on Field-Programmable Gate Array
- 1. IJSRD - International Journal for Scientific Research & Development| Vol. 1, Issue 5, 2013 | ISSN (online): 2321-0613 All rights reserved by www.ijsrd.com 1093 Abstract--In this paper fully parallel FIR filters are designed with different design method on FPGA for resource utilization and response analysis. fully parallel band-pass FIR filters with same specification designed and simulated on ISE. The suggested implementations are synthesized with Xilinx ISE 14.2 version. Results show comparison of three different filter design methods in terms of resource utilization. I. INTRODUCTION Digital filters are important part of digital signal processing. Before development of FPGA digital filter were implemented on digital signal processor. Digital signal processors are still widely used but they are not capable for high speed application available in present. After the advancement of microelectronic techniques, communication signal processing has come to third generation and forth generation period, so there is a challenge for adaptive processing techniques that the processing speed needs to be high so FPGA based signal processing techniques is mostly used in latest mobile communication, military communication, consumer electronics and aerospace tracking etc so that It is necessary to find the answer of how to increase operation speed of signal processing algorithms and reduce hardware resources by adopting FPGA to implement every kinds of tasks of digital signal processing. So we look forward for design of digital filter with low area and high speed. Benefits of reducing area: (a) Less power required (b) Area benefits for other application on same chip (c) We can use versions of FPGA which have less capability. Digital filters are typically used to modify or alter the attributes of a signal in the time or frequency domain. The most common digital filter is the linear time-invariant (LTI) filter. An LTI interacts with its input signal through a process called linear convolution, denoted by y = f * x where f is the filter's impulse response, x is the input signal, and y is the convolved output. The linear convolution process is [1] formally defined by: y[n] = x[n] * f[n] = ∑ [ ] [ ] = ∑ [ ] [ ] (1)[1] LTI digital filters are generally classified as being finite impulse response (i.e., FIR), or infinite impulse response (i.e., IIR). Calculating the constant coefficients of such a digital filter involves considerable amount of computation and this is generally performed using software tools [1]. With available digital filter design software the production of FIR coefficients is a straightforward process. The Filter Design and Analysis (FDA) tool packaged along with MATLAB is such a tool. The double length floating point notation for filter coefficients, used by the FDA tool poses immense challenges in terms of cost and resources, while implementing on an FPGA [1]. The challenge remains is to map the FIR design into a suitable architecture. To overcome this, the filter coefficients have to be quantized to a fixed point notation. The result of coefficient quantization is that the actual implemented transfer function is different from the ideal transfer function. The simplest and most widely used approach to the problem is to round off the optimal infinite precision coefficients to a b-bit representation [1]. II. PARALLEL AND SERIAL ARCHITECTURES The basic equation for a single-channel FIR filter is shown in equation [1] ( ) ∑ ( ) ( ) (2) The terms in the equation can be described as input samples, output samples, and coefficients. Imagine x(n) as a continuous stream of input samples and y(n) as a resulting stream (i.e., a filtered stream) of output samples[1]. The n and k in the equation correspond to a particular instant in time, so to compute the output sample y(n) at time n, a group of input samples at N different points in time, or x(n), x(n-1), x(n-2), ... x(n-N+ 1) is required[1]. The group of N input samples are multiplied by N coefficients and summed together to form the final result y(n).Fig. 1 shows the logical structure of an FIR Filter[1]. Fig. 1: Logical Structure of an FIR filter [1] A fully parallel architecture uses a dedicated multiplier and adder for each filter tap; all taps execute in parallel, thereby creating fully parallel implementation. This architecture is optimal for speed. However, it requires more multipliers and adders than a serial architecture, and therefore consumes more chip area. Fig. 2 shows the fully parallel architecture of 64 tap FIR Filter [1]. Analysis of different FIR Filter Design Method in terms of Resource Utilization and Response on Field-Programmable Gate Array Nilesh B. Bosmiya1 Prof. R. C. Patel2 1 PG Student 2 Professor 1, 2 Dept. of Instrumentation & Control, L. D. College of Eng. Gujarat, India
- 2. Analysis of different FIR Filter Design Method in terms of Resource Utilization and Response on Field-Programmable Gate Array (IJSRD/Vol. 1/Issue 5/2013/0014) All rights reserved by www.ijsrd.com 1094 Fig. 2: Parallel implementation of FIR filter [1] III. FPGA SIMULATION AND RESULT COMPARISON An FIR Band Pass filter is designed as per the specifications given in table 1. With three different design method which are Equiripple, Least-Squares, Least Pth-norm. A special class of FIR filter that is particularly effective in meeting Frequency Value Sampling Frequency 48000Hz Stop band Frequency1 7250Hz Pass band Frequency1 9650Hz Pass band Frequency2 12050Hz Stop band Frequency2 14450Hz Stop band Attenuation1 80 dB Pass band Attenuation 1 dB Stop band Attenuation2 80 dB Table. 1: Filter Specifications Fig. 3: Response for reference filter with Equiripple design Fig. 4: Response of the filter with Least-Squares design Such specifications are called the equiripple FIR filter. An equiripple design protocol minimizes the maximal deviations (ripple error) from the ideal transfer function. The filer designed for the mentioned specifications using equiripple design method is of order 64[1]. Fig. 3 is for the response of the filter with Equiripple design. Fig. 4 is for the response of the filter with Least-Squares design. Fig. 5 is for the response of the filter with Least Pth Norm design. Fully parallel and filter was designed and its behavioural simulation was done using Xilinx ISE 14.2. Resource utilization for different filter design method is shown in table 2. Fig. 5: response of the filter with Least Pth-Norm design
- 3. Analysis of different FIR Filter Design Method in terms of Resource Utilization and Response on Field-Programmable Gate Array (IJSRD/Vol. 1/Issue 5/2013/0014) All rights reserved by www.ijsrd.com 1095 Fig. 6: Waveform screenshot of software simulation for fully parallel design Equiripple Least- Squares Least Pth- Norm Quantization Q16.14 Q16.14 Q16.14 Slices 2651 2797 2798 Slice Flip Flops 1055 1055 1055 LUTs 4065 4358 4328 Max .Freq. (MHz) 7.378MHz 7.373MHz 7.548MHz Table. 2: Resource utilization for different filter design method Now the Starting portion of simulation result is shown in Fig. 6. IV. CONCLUSION We can clearly see that from table II and response figures equiripple design is superior than other two methods. ACKNOWLEDGEMENTS Author thanks Prof. R. C. Patel for his valuable guidance for this paper. Author is also thankful to his staff and colleagues for their co-operation. REFERENCES [1] V. Sudhakar, N. S .Murthy, L. Anjaneyulu, “fully parallel and fully serial architecture for realization of high speed FIR filters with FPGA’s Devices, Circuits and Systems (ICDCS)” , 2012 International Conference on Digital Object Identifier: 10.1109/ICDCSyst.2012.6188766 Publication Year: 2012, Page(s): 499 - 501 IEEE Conference Publications. [2] Vinger K. and Torresen J, "Implementing Evolution of FIR filters efficiently in an FPGA", Proc. of2003 NASA/DoD Conference on Evolvable Hardware (EH- 2003), July, 2003, Chicago, Illinois, USA [3] Shanthala S, and S. Y. Kulkarni, "High Speed and Low Power FPGA Implementation of FIR Filter for DSP Applications" European Journal of Scientific Research, 2009. [4] Wonyong Sung and Ki-Il Kum, "Simulation Based Word-Length Optimization Method for Fixed-point Digital Signal Processing Systems", IEEE Transactions on Signal Processing,Vo. 43, No.12, December 1995. [5] X. Hu, L. S. DeBrunner, and V. DeBrunner, "An efficient design for FIR filters with Variable precision", Proc. 2002 IEEE Int. Symp. On Circuits And System. [6] S. K. Mitra, “Digital Signal Processing: A computer- Based Approach ”, 2nd ed. McGraw-Hill, 1997. [7] U. Meyer-Baese, “Digital Signal Processing with Field Programmable Gate Arrays”, Springer, 2004.