International Journal of Engineering Trends and Technology (IJETT) – Volume 4 Issue 9- Sep 2013
A Review on Speech Denoising Using
Wavelet Techniques
KamyaDubey#, Prof. Vikas Gupta*
Department of Electronics and Communication, T.I.T, R.G.P.V., Bhopal
Abstract- The use of wavelet transform for denoising speech
signals contaminated with common noises.The basic principles
of wavelet transform hold good promise an alternative to the
Fourier transform. Based on the fact that noise is the main
factor that limit the capacity of data transmission in
telecommunications and that also affect the accuracy of the
results in the signal measurement systems, whereas, modeling
and removing noise and is at the core of theoretical and
practical considerations in communications and signal
processing. In this paper Wavelet for noise removal has been
discussed.
Keywords: Wavelet,Daubechies,Coiflet,De-noising.
I. INTRODUCTION
Speech is a very basic way for humans to
conveyinformation to one another. With a bandwidth of only
4 kHz, speech can convey information with the emotion of a
human voice. People want to be able to hear someone's voice
from anywhere in the world, as if the person was in the same
room. As a result a greater emphasis is being placed on the
design of new and efficient speech coders for voice
communication and transmission.
Human Speech signal are in acoustic signal form so for the
purpose of communication it’s a necessary to convert into the
electrical signal with the help of instruments called
‘Transducers’. Electrical representation of speech signal has
same properties, such as:
1. It is a one-dimensional signal, with time as its independent
variable.
2. It is random in nature.
3. It is non-stationary, i.e. the frequency spectrum is not
constant in time.
4. Although human beings have an audible frequency range
of 20Hz - 20 kHz,
The wavelet transform is similar to the Fourier transform.
For the FFT, the basis functions are sines and cosines. For
the wavelet transform, the basis functions are more
complicated called wavelets, mother wavelets or analyzing
wavelets and scaling function. In wavelet analysis, the signal
is broken into shifted and scaled versions of the original (or
mother) wavelet. The fact that wavelet transform is a multi
resolution analysis makes it very suitable for analysis of nonstationary signals such as audio signals.
II. WAVELETS
A wavelet is a finite energy signal defined over specific
interval of time [1]. The main interest in wavelets is their
ability to represent a given signal at different. Wavelets are
used to analyze signals in much the same way as complex
exponentials (sine and cosine) used in Fourier analysis of
signals. Unlike Fourier, wavelets can be used to analyze
nonstationary, time-varying, or transient signals [9] [10].
This is an important aspect, since speech signals are
considered to be non-stationary. A given signal is represented
by using translated and scaled versions of a mother wavelet .
Wavelets are characterized by scale and position, and are
useful in analyzing variations in signals in terms of scale and
position. Because of the fact that the wavelet size can vary, it
has advantage over the classical signal processing
transformations to simultaneously process time and
frequency data. The general relationship between wavelet
scales and frequency is to roughly match the scale. At low
scale, compressed wavelets are used. They correspond to
fast-changing details, that is, to a high frequency. At high
scalethe wavelets are stretched. They correspond to slow
changing features, that is, to a low frequency.
A. Continuous Wavelet Transform
The wavelet transform is a two parameter expansion of a
signal in terms of a particular wavelet basis function [1].
Given Ψ(t) called the mother wavelet; all other baby wavelets
are obtained by simple scaling and translation of Ψ(t). Ψa,t(t)
= (1/√a) Ψ[(t-b)/a]. Where a and b are the scaling and the
translation parameter respectively. A nice approach to the
CWT representation is first to inspect the Fourier transform
represented mathematically by:
F(ω) = ∫s(t)e-jωtdt…………..(1)
Replacing the complex exponential in the Fourier transform
with Ψa,t(t) yields:
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International Journal of Engineering Trends and Technology (IJETT) – Volume 4 Issue 9- Sep 2013
C(S,U) = ∫√a Ψ[(t-b)/a]dt……….(2)
In other words with wavelet transform, reference to
frequency is replaced by reference to scale [8], [9][10].
B. Discrete Wavelet Transform
In our application the discrete wavelet transform is
applied.By choosing scale and position based on power of 2,
CWT isreduced to DWT without any loss in energy. The
scalingparameter is discrete and dyadic, a = 2-j. The
translation isdiscretized with respect to each scale by using τ
= k2-jT [5].Ψj,k(t) = (2j/2) Ψ[(2jt-kT)].The integer k
represents the translation of the waveletfunction; it indicates
time in wavelet transform. Integer j,however, is an indication
of the wavelet frequency orspectrum shift and generally
referred to as scale. The DWTtransforms a discrete input
signal vector into two sets ofcoefficients the approximation
CA containing low frequencyinformation and the detail
coefficients CD containing highfrequency information. Fig. 1
shows a level 2 DWTdecomposition of an input signal s (t)
[8] [9] [10].
Figure.3: IDWT Reconstruction (Synthesis)
III. NOISE
Noise is defined as an unwanted signal that interferes with
the communication or measurement of another signal. A
noise itself is an information-bearing signal that conveys
information regarding the sources of the noise and the
environment in which it propagates. Noise can be categorized
of different types .In which white noise is defined as an
uncorrelated random noise process with equal power at all
frequencies. Random noise has the same power at all
frequencies in the range of ∞ it would necessarily need to
have infinite power, and it is therefore an only a theoretical
concept. However, a band-limited noise process with a flat
spectrum covering the frequency range of a band-limited
communication system is practically considered a white noise
process.
Figure .1: Plots of Different Daubechies Orthogonal Wavelets
Figure .2: DWT Decomposition (Analysis)
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International Journal of Engineering Trends and Technology (IJETT) – Volume 4 Issue 9- Sep 2013
Figure.4: Sine wave with added white noise.
IV.RESULT
used as denoising technique. We have compared different
wavelet families: Daubechies and Coiflets, and we used
cross-correlation to determine the best fit between an original
signal and the processed one. By using Coiflet 5, Daubechies
9 and 10 we obtained the best result because they have a
higher correlation at zero.
An audio signal is selected and with wavelets coif5, db9 and
db10.denoising and cross correlation is performed. Figure
shows the original audio signal, audio signal with noise and
the recovered signal using the wavelet.
Figure.5:Cross correlation of original signal and signal de-noise
REFERENCES
[1] Y. T. Chan “Wavelet Basics”, Kluwer Academic Publishers, 1995.
[2] C. Taswell, “Speech Compression with Cosine and Wavelet Packet NearBest Bases”, ICASSP-96. Conference Proceedings, IEEE International
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[3] E. Fgee, W. J. Phillips, W.Robertson “Comparing Audio Compression
Using Wavelets With Other Audio Compression Schemes”, IEEE,
CCECE Conference Edmonton, Alberta, Canada. May 9-12, pp: 698701, 1999.
[4] N. M. Hosny, S. H. El-Ramly, M. H. El-Said, “Novel Techniques for
Speech Compression Using Wavelet Transform”, ICM '99. 11th
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[5] http://www.mathworks.com/academia MATLAB Wavelet Toolbox 2.
[6] O. Rioul and M. Vetterli, “Wavelets and Signal Processing”, IEEE
Signal Process. Mag. Vol 8, pp. 14-38, Oct. 1991.
[7] J. I. Agbinya, “Discrete Wavelet Transform Techniques in Speech
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Proceedings,IEEE, New York, pp: 514 – 519, 1996.
[8] J. F. Koegel Buford, “Multimedia Systems”, ACM Press, 1994.
[9] G. Strang and T. Nguyen, “Wavelets and Filter Banks”, WellesleyCambridge Press, 1996.
[10] J. S. Walker, “Wavelets and their Scientific Applications”, Chapman
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Figure.6: Original audio signal, audio signal with noise
and the recovered signal
V.CONCLUSION
Practical approach in how to put into practice wavelets in
noisy audio data to improve clarity and signal retrieval has
been discussed. analysis.Fourier transform based spectral
analysis is the dominant analytical tool for denoising of audio
signal.
However, Fourier transform cannot provide any
information of the spectrum changes with respect to time.
Fourier transform assumes the signal is stationary, but audio
signal is always non-stationary. To overcome this wavelet is
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