Improving the Efficiency of Spectral Subtraction Method by Combining it with Wavelet Thresholding Technique

International Journal of Research in Computer Science
eISSN 2249-8265 Volume 3 Issue 3 (2013) pp. 29-33
www.ijorcs.org, A Unit of White Globe Publications
doi: 10.7815/ijorcs. 33.2013.065
www.ijorcs.org
IMPROVING THE EFFICIENCY OF SPECTRAL
SUBTRACTION METHOD BY COMBINING IT WITH
WAVELET THRESHOLDING TECHNIQUE
G. R. Mishra1
, Saurabh Kumar Mishra2
, Akanksha Trivedi3
, O.P. Singh4
, Satish Kumar5
*Department of ECE, Amity School of Engineering & Technology, Amity University, Lucknow Campus, INDIA
Email: 1
grmishra@gmail.com, 2
saurabhmishra18@gmail.com, 3
akanksha2trivedi@gmail.com
Abstract: In the field of speech signal processing,
Spectral subtraction method (SSM) has been
successfully implemented to suppress the noise that is
added acoustically. SSM does reduce the noise at
satisfactory level but musical noise is a major
drawback of this method. To implement spectral
subtraction method, transformation of speech signal
from time domain to frequency domain is required. On
the other hand, Wavelet transform displays another
aspect of speech signal. In this paper we have applied
a new approach in which SSM is cascaded with
wavelet thresholding technique (WTT) for improving
the quality of speech signal by removing the problem
of musical noise to a great extent. Results of this
proposed system have been simulated on MAT LAB.
Keywords: Coefficient Thresholding, Musical Noise,
SSM, Wavelet Coefficients, WTT.
I. INTRODUCTION
The musical noise produced by SSM is a major
drawback of this system, but there are so many
methods that have been given for musical noise
reduction. This paper proposed a new technique in
which SSM is cascaded with WTT for musical noise
reduction.
SSM requires a transformation of signal from time
domain to frequency domain using FFT. In this
method, a voice activity detector [1] is used for
detecting the signal whether it is voiced signal or
unvoiced signal. This method is based on the direct
estimation of the short term spectral magnitude of
speech signal during non-speech activity. Spectral
subtraction method is successful in stationary or
slowly varying noisy environment, otherwise the
estimated noise is not correct and system generates
musical noise [10]. On the other hand, if we transform
a signal into wavelet domain it simply breaks the
signal into low frequency and high frequency
components with the help of low pass filter and high
pass filter that yields the coefficients. In this method, a
thresholding technique is used for signal de-noising
that discards the coefficients below threshold level.
WTT [7] has been successfully used for image de-
noising but a very less attention has been paid for
practical implementation of this technique in the field
of speech signal. WTT can de-noise [2] a signal
without noticeable loss because it reveals the aspects
like trends, breakdown points, discontinuities in higher
derivatives. In this paper we have cascaded [8] WTT
with spectral subtraction method because both
techniques use different approach for signal de-
noising. First we applied SSM and then the output of
SSM is given as input in WTT for better results. This
new method will be very effective for military
applications, real time noisy environments.
II. SPECTRAL SUBTRACTION METHOD (SSM)
A. Introduction
SSM is very popular and useful for acoustic noise
suppression because of its relative simplicity and ease
of implementation. This method is used for restoration
of power spectrum or magnitude spectrum of a speech
signal contains additive noise. In this method, a noise
is added acoustically or digitally into the original
speech signal and it becomes noisy speech signal.
Then we take an estimation of the noise spectrum that
updated from the periods during non-speech activity
when only noise is present. The estimation of noise
spectrum is subtracted from noisy signal and then we
get an estimate of the clean reconstructed signal.
Generally, spectral subtraction is effective for
stationary or slowly varying noisy environments.
B. Mathematical Approach
Suppose speech signal 𝑥(𝑚) is corrupted by noise
𝑛(𝑚) that yields noisy signal
𝑌(𝑚) = 𝑥(𝑚) + 𝑛(𝑚) … (1)
When windowing the signal
𝑌𝑤(𝑚) = 𝑥 𝑤(𝑚) + 𝑛 𝑤(𝑚) ... (2)
Fourier transform of equation (2) is as under
𝑌𝑤(𝑒 𝑗𝑤
) = 𝑋 𝑤(𝑒 𝑗𝑤) + 𝑁 𝑤(𝑒 𝑗𝑤) … (3)

30 G. R. Mishra, Saurabh Kumar Mishra, Akanksha Trivedi, O.P. Singh, Satish Kumar
www.ijorcs.org
Where 𝑌𝑤(𝑒 𝑗𝑤
), 𝑋 𝑤�𝑒 𝑗𝑤
�and 𝑁 𝑤(𝑒 𝑗𝑤
) are the
Fourier transforms of noisy speech, original speech,
and noise signals respectively.
For simplification purpose w (windowed) notation
is dropped.
When multiplying both sides by their complex
conjugates, we find
[𝑌(𝑒 𝑗𝑤
)]2
=
[𝑋(𝑒 𝑗𝑤
)]2
+ [𝑁(𝑒 𝑗𝑤
)]2
+ 2[𝑋(𝑒 𝑗𝑤)][𝑁(𝑒 𝑗𝑤)]𝑐𝑜𝑠𝐷𝑞 …
(4),
Where, 𝐷 𝑞 stands for phase difference between
speech signal and noise signal.
( ) ( )j j
qD X e N eω ω
= ∠ − ∠ ….. (5)
We take expected value on both sides of equation (4)
𝐸{[𝑌(𝑒 𝑗𝑤)]2} = 𝐸{[𝑋(𝑒 𝑗𝑤)]2
} + 𝐸{[𝑁(𝑒 𝑗𝑤)]2
}
+ 2𝐸{[𝑋(𝑒 𝑗𝑤)]}𝐸{[𝑁(𝑒 𝑗𝑤)]}𝐸{cos(𝐷𝑞)}
…… (6)
1. Power spectral subtraction:
For power spectral subtraction it is assumed that
{ }cos 0qE D =
, hence equation (6) becomes
𝐸{[𝑌(𝑒 𝑗𝑤)]2
} = 𝐸{[𝑋(𝑒 𝑗𝑤)]2
} + 𝐸{[𝑁(𝑒 𝑗𝑤)]2
}
So, [𝑋(𝑒 𝑗𝑤)]2
= [𝑌(𝑒 𝑗𝑤)]2
− 𝐸{[𝑁(𝑒 𝑗𝑤)]2
.... (7)
2. Magnitude spectral subtraction:
For magnitude spectral subtraction it is assumed
that { }cos 1qE D = , hence equation (6) becomes
𝐸{[𝑌(𝑒 𝑗𝑤)]2} = 𝐸{[𝑋(𝑒 𝑗𝑤)]2} + 𝐸{[𝑁(𝑒 𝑗𝑤)]2}
+ 2𝐸{[𝑋(𝑒 𝑗𝑤)]}𝐸{[𝑁(𝑒 𝑗𝑤)]}
𝐸{[𝑌(𝑒 𝑗𝑤)]} = 𝐸{[𝑋(𝑒 𝑗𝑤)]} + 𝐸{[𝑁(𝑒 𝑗𝑤
)]}
[𝑋(𝑒 𝑗𝑤)] = [𝑌(𝑒 𝑗𝑤)] − 𝐸{[𝑁(𝑒 𝑗𝑤)]} ….. (8)
The procedure of spectral subtraction method
has been shown below in figure 1.
𝑁𝑜𝑖𝑠𝑦 𝑠𝑖𝑔𝑛𝑎𝑙 𝑦(𝑚)
𝑥�(𝑚)
Figure1: Basic blocks of spectral subtraction method
III. WAVELET THRESHOLDING TECHNIQUE
(WTT)
A. Introduction
SSM is effective for stationary or slowly varying
noises, but in mobile communication, signal is
definitely not stationary. So the next possible
improvement in speech signal is to further decrease the
problem of musical noise using WTT. In wavelet
transform the output speech signal 𝑥�(𝑚) of spectral
subtraction method has been taken as an input signal
and that signal is divided up into low frequency and
high frequency components. The output of LPF is
known as approximation coefficients and the output of
HPF is called detail coefficients. When we analyze
approximation coefficients [9] at level 1 by using
MATLAB command sound (cA1, Fs, bit depth) we
can understand the speech with a low loss in the
quality of signal. This shows that low frequency
components contain essential information and that is
why the output of LPF is called approximation
coefficient. The output of HPF contains only high
frequency non-essential information and is known as
detail coefficient. For applying wavelet technique first
we have to choose an appropriate mother wavelet and
level of decomposition of the signal. Choosing a
mother wavelet depends on the type of the signal we
have to decompose. While speech de-noising our
objective is to improve quality of the signal, so
wavelet can be selected on the basis of energy
conservation properties in the approximation
coefficients [7]. By using Daubechies D20, D6, D4,
D2 or Haarwavelets, more than 90% of the signal
energy, level 1 approximation coefficients contains.
For selecting a decomposition level, if the frame based
input is applied, then frame size must be a multiple
of 2 𝑛
, where n represents the decomposition level. In
this paper, we have selected ‘Daubechies’ as a mother
wavelet and decomposition level is 6.
B. Wavelet approach for musical noise reduction
Wavelet thresholding technique is very useful and a
different technique for residual noise reduction.
Residual noise come into existence because of
variation in background noise, and that is why residual
noise occurs during whole speech (including speech
activity as well as non- speech activity). Using wavelet
thresholding technique we are exploiting the fact that
residual noise contains narrower peaks which are
relatively high frequency components. More than 90%
components of speech signal have values zero or near
to zero that is clear from histogram representation.
Here a threshold value is selected and all the
coefficients are truncated that have values lower than
threshold, so wavelet thresholding technique removes
residual noise (also called musical noise in time
domain) successfully to the great extent.
FFT SSM IFFT

Improving the Efficiency of Spectral Subtraction Method by combining it with Wavelet Thresholding Technique 31
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Figure2: Histogram representation
IV. THRESHOLDING OF COEFFICIENTS
After applying wavelet transform, input signal is
decomposed into coefficients. Then we perform
thresholding of coefficients for signal de-noising
which is of two types, hard thresholding and soft
thresholding. Generally hard thresholding is used for
signal compression and soft thresholding is used for
signal de-noising. Here we have used soft thresholding
for de-noising the signals. Soft thresholding is an
expansion of hard thresholding in which we first set to
zero the elements whose absolute values are lesser
than the threshold and then shrink the nonzero
coefficients toward 0. After choosing soft
thresholding, there are two types for finding a
threshold value named global thresholding and level
dependent thresholding. In global thresholding, a
threshold value is set manually. For level dependent
thresholding, we use Brige-Massart strategy [7] that
yields a different threshold values for each level. To
de-noise a signal we use a MATLAB command
wdencmp that enables us to choose between global and
level dependent thresholding. Coefficient thresholding
discards the coefficient that has a value below the
threshold and it results de-noised signal. In wavelet de-
noising method we have taken 𝑥�(𝑚) as an input signal
that is output signal of SSM. Steps involved in wavelet
de-noising process are shown in figure 3.
𝑥�(𝑚)
Figure3: Wavelet de-noising process
V. PERFORMANCE ANALYSIS OF PROPOSED
SYSTEM
Performance analysis of this proposed system has
been done in terms of Peak signal to noise ratio
(PSNR) and Normalized root mean square error
(NRMSE).
PSNR has been evaluated using
𝑃𝑆𝑁𝑅 = 10𝑙𝑜𝑔10
𝑁𝑋2
‖𝑥 − 𝑟‖2
Where, N is the length of the reconstructed signal,
X is the maximum absolute square value of signal
x. ‖𝑥 − 𝑟‖2
is the energy of the difference between
original and reconstructed signal.
And NRMSE has been evaluated using
𝑁𝑅𝑀𝑆𝐸 = �
(𝑥(𝑛) − 𝑟(𝑛))2
(𝑥(𝑛) − 𝜇𝑥(𝑛)2
Where, 𝑥(𝑛) is the speech signal, 𝑟(𝑛) is the
reconstructed signal and 𝜇𝑥(𝑛) is the mean of the
speech signal.
For better results PSNR should be higher while
value of NRMSE should be as low as possible.
We have taken a male spoken speech signal of 5 sec
with 8 KHz sampling frequency and bit depth is 16,
shown in figure4
Figure 4: Original speech signal
After digitally added random noise in original speech signal,
the noisy speech signal is shown in figure 5
Figure5: Noisy signal
Select a
mother
wavelet
Wavelet de-
composition
Thresholding
& truncation
Wavelet
reconstructionFinal O/P signal

32 G. R. Mishra, Saurabh Kumar Mishra, Akanksha Trivedi, O.P. Singh, Satish Kumar
www.ijorcs.org
We applied SSM for signal de-noising and got
reconstructed signal shown in figure 6.
Figure 6: Output de-noised signal of spectral subtraction
After getting the output de-noised signal using
SSM, we used command sound (reconstructed signal,
Fs, bit depth) to hear the de-noised signal and got a
great improvement in the quality of signal (PSNR and
NRMSE of 𝑥�(𝑚) using SSM is 13.4981dB and
1.0818) but a little bit presence of noise still we can
feel that is identified by musical noise. So we have
used a new technique for reducing musical noise in
which the reconstructed signal using SSM is taken as
input signal for WTT. After transforming this signal
into wavelet coefficients and applying thresholding
respectively we got an output signal with reduced
musical noise. This final output signal with reduced
musical noise is shown in figure 7.
Figure 7: Signal of reduced musical noise using haar
wavelet
Table (a)
Wavelet
type
Decomp
-osition
level
Percentage
Retained
energy
PSNR in
dB
NRMS
E
Haar 6 83.7857 14.4836 1.0298
Db2 6 86.5747 14.3677 1.0357
Db4 6 87.9903 14.2931 1.0396
Db6 6 88.5790 14.2650 1.0411
PSNR using SSM is 13.4981dB, and NRMSE using
SSM is 1.0818 and the PSNR and NRMSE values
given in table (a) have been observed using proposed
new system (SSM+WTT). So it’s clear from PSNR
and NRMSE values that there is a significant
improvement in the speech signal by cascading SSM
withWTT.
Figure 8: Performance evaluation based on PSNR
Figure 9: Performance evaluation based on NRMSE
VI. CONCLUSION AND FUTURE SCOPE
Musical noise is a problem of spectral subtraction
method that has been eliminated using wavelet
thresholding technique (WTT). In this paper we have
proposed a new system (SSM+WTT) which combined
SSM and WTT respectively and the efficiency of the
proposed system is higher as compared to SSM. Result
of this combined system is clear from the waveform
shown in figure 7 and differences between PSNR and
NRMSE values. Table (a) represents the type of
mother wavelet, decomposition level, percent retained
signal energy in de-noised signal, peak signal to noise
ratio (PSNR) and NRMSE. Haar wavelet has highest
PSNR and lowest NRMSE values. Results have been
simulated on MATLAB.
In future, if we use Wavelet Packet Transform
instead of Wavelet transform with adaptive
thresholding technique, the quality of reconstructed
speech signal will be better.
VII. REFERENCES
[1] S. F. Boll, “Suppression of acoustic noise in speech,
using spectral subtraction” .IEEE. Acoustic.Speech,
Signal Processing, vol. ASSP-27, pp. 113-120, Apr.
1979. doi: 10.1109/TASSP.1979.1163209
[2] Ing Yann Soon Soo Ngee Koh Cii Kiat Yeo, “Wavelet
For Speech De-noising”, 1997 IEEE Tencon - Speech
and Image Technologies for Computing and
Telecommunications.
13
13.5
14
14.5
PSNR IN dB
Haar
Db2
Db4
Db6
SSM
1
1.02
1.04
1.06
1.08
1.1
NRMSE
Haar
Db2
Db4
Db6
SSM

Improving the Efficiency of Spectral Subtraction Method by combining it with Wavelet Thresholding Technique 33
www.ijorcs.org
[3] Soltani Bozchalooi, Ming Liang, “A Combined Spectral
Subtraction and Wavelet De-Noising Method for
Bearing Fault Diagnosis”, IEEE Amercian Control
Conference, pp 2533-2538, 2007. doi:
10.1109/ACC.2007.4282467
[4] Talbi Mourad, Cherif Adnene, “Simulation and
comparison of noise cancellation technique in speech
processing”, IEEE Electrotechnical Conference, pp
541-544, 2006. doi: 10.1109/MELCON.2006.1653158
[5] Wilfred N Mwema and Elijah Mwangi, “A Spectral
Subtraction Method for Noise Reduction in Speech
Signals”, IEEE AFRICON 4th
, pp 382-385. 1996. doi:
10.1109/AFRCON.1996.563142
[6] Saeed V. Vaseghi “Advanced Digital Signal Processing
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84162-1 (Electronic). doi: 10.1002/0470841621
[7] Nikhil Rao, “Speech Compression Using Wavelets”,
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[8] WANG Guang-yan, ZHAO Xiao-qun, WANG Xia,
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Subtraction Combined with Wiener Filtering for Speech
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[9] Satish Kumar, O.P. Singh, G.R. Mishra, Saurabh
Kumar Mishra, Akanksha Trivedi “Speech
Compression and Enhancement using WaveletCoders”,
International Journal of Electronics Communication and
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(Online): 2249–071X, ISSN (Print): 2278–4209.
[10] James R. Hamilton, “Musical Noise”, British Journal of
Aesthetics, Vol. 39, No. 4, October lag, pp 350-363.
doi: 10.1093/bjaesthetics/39.4.350
[11] Ben Gold and Nelson Morgan. 'Speech and Audio
Signal Processing'. John Wiley and Sons, 2000.
[12] Jr. J.R. deller, J. Hansen and J.G. Proakis, “Discrete-
time processing of speech signals”, IEEE press, New
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[13] Chin-Teng Lin, “Single-channel speech enhancement in
variable noise-level environment”, Systems, Man and
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pp 137–143, Jan. 2003. doi: 10.1109/TSMCA.
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How to cite
G. R. Mishra, Saurabh Kumar Mishra, Akanksha Trivedi, O.P. Singh, Satish Kumar, "Improving the Efficiency
of Spectral Subtraction Method by combining it with Wavelet Thresholding Technique". International Journal
of Research in Computer Science, 3 (3): pp. 29-33, May 2013. doi: 10.7815/ijorcs. 33.2013.065

Improving the Efficiency of Spectral Subtraction Method by Combining it with Wavelet Thresholding Technique

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