e-ISSN: 2582-5208 International Research Journal of Modernization in Engineering Technology and Science Volume:03/Issue:03/March-2021
Impact Factor- 5.354
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SPEECH ANALYSIS AND DENOISING USING WAVELETS Palle Praneeth*1, Parankusham Ramyaja Shreeya*2 *1PG
Scholar, Department of Electronics & Communication Engineering, JNTUH College of Engineering, Hyderabad, Telangana, India.
*2PG
Scholar, Department of Electronics & Communication Engineering, JNTUH College of Engineering, Hyderabad, Telangana, India.
ABSTRACT All long-distance speech communications (in planes, helicopters, trains etc.,) have distortions in signal due to noise. So, analysis of speech signal and removal of noise plays an important role in communication. In this paper we discuss about how to denoise the signal using Discrete Wavelet Transform (DWT). Although there are many ways of denoising by using FT, FFT, STFT etc., there are certain limitations to them because of which we prefer denoising the signal using DWT. In DWT we do denoising using soft thresholding (ST), where values for positive and negative coefficients are shrinked towards zero. Keywords: Discrete wavelet Transform, Thresholding, Wavelet Decomposition.
I.
INTRODUCTION
The Wavelet transform provides the time and frequency information simultaneously. So more detailed analysis of signal is possible and optimistic results can be achieved. As in its continuous form it produces huge data and computational work, to reduce them the Discrete Wavelet Transform is introduced. Here equation(1) represents Mother Wavelet Function, where a is scaling parameter, b is translation parameter, equation(2) represents Continuous Wavelet Transform(CWT), equation(3) represents Discrete Wavelet Transformation.
( )
√
((
) )…………. eq (1)
( )>=∫
CWT(a,b)=<f(x),
a=
( )
( )
( )
………eq (2)
, where
b=n
where ( )
DWT(m,n)=<f,
(
(
>=
))
∑
( )
(
)………eq (3)
There are many different types of Wavelets and they are chosen as per the requirement. Here we divide speech signal into different frequencies and study them and apply Soft thresholding and reconstruct the signal. Noise signal which has low Lipschitz index and different singularities is observed based on which universal threshold value is calculated to denoise.
II.
METHODOLOY
Using Wavelets Decomposition of Noisy signal Denoise of a signal is done in an iterative manner i.e., as number of iterations increases the better perfection can be seen. Equation (4) and equation (5) represents decomposition of signals using high pass filter for detailed coefficients and low pass filter for approximate coefficients which are down sampled by 2. Next approximate coefficients are further decomposed into approximate coefficients and detailed coefficients. This www.irjmets.com
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e-ISSN: 2582-5208 International Research Journal of Modernization in Engineering Technology and Science Volume:03/Issue:03/March-2021
Impact Factor- 5.354
www.irjmets.com
process is carried out N number of times as per the requirement. Even though decomposition is done we still have noise in the signal which is why we go for thresholding of the signal.
∑
………. eq (4)
∑
…………eq (5)
Level 1 Level 3 0-500 Hz
LPF
Signal
500-750 Hz
500-1000 Hz
HPF
LPF
750-825 Hz
HPF
825-1000 Hz
750-1000 Hz
Level 2 1D Wavelet Decomposition up to three levels Mother Wavelet
There are many types of mother wavelets like Haar, Meyer, Morlet, Dabechies etc., .Here we use Symlet 8 Wavelets which are approximate symmetrical wavelets proposed by Daubechies. They are modification of Daubechies families. They are also commonly known as Modified Daubechies Wavelets.
Figure-1: Symlet 8 Wavelet
Thresholding the noisy signal Here, we use universal thresholding method to find the threshold value which is given by equation (6) Threshold = (2log(N))-1/2
σ= (1/0.6745) median (dj) After finding the threshold value we should choose threshold method. There are two types of thresholding methods- Soft Thresholding and Hard Thresholding. Hard Thresholding means discarding and assigning zero to the coefficients which are less then the thresholding value. In Soft Thresholding the coefficients which are less than threshold value are reduced, the reduction is large for large coefficients and small for small coefficients. Here we use soft thresholding method. After filtering, the signal is reconstructed with the last approximate coefficient and all detailed coefficients. To measure the amount of filtering after the reconstruction signal to noise ratio is applied. www.irjmets.com
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e-ISSN: 2582-5208 International Research Journal of Modernization in Engineering Technology and Science Volume:03/Issue:03/March-2021
Impact Factor- 5.354
www.irjmets.com
Figure-2. Hard thresholding and Soft thresholding graphs
III.
RESULTS AND DISCUSSION
Here, the results are broken down into decomposition coefficients graphs, scalogram, original speech signal, mixed signal with noise and speech signal, final denoised graph, SNR ratio.
Figure-3: Original signal without any noise
Figure 4. Noisy signal where additive noise is added to the signal
Figure-5: S is denoised signal and d1,d2,d3,d4,d5 are detailed coefficients and a5 is approximate coefficient
As we observe in the figure(3) d1 which represents detailed coefficient of 1st decomposition and d5 which represents detailed coefficient of 5th decomposition have huge disparity when compared with the original signal which is in figure(4). We can see that as the number of decompositions increases the noisy signal is more tending towards perfection.
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e-ISSN: 2582-5208 International Research Journal of Modernization in Engineering Technology and Science Volume:03/Issue:03/March-2021
Impact Factor- 5.354
Figure-6: Filtered signal
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Figure-7: Scalogram
Level of decomposition
SNR (in db)
Threshold Values
1st
1.801
0.183
3.263
0.166
level
7.218
0.289
4th level
9.662
1.087
5th level
12.301
1.419
level
2nd 3rd
level
Figure(6) the filter signal we obtained a after reconstruction of the noisy signal, before filtering of the signal the signal to noise ratio is 1.034 db and after denoising the SNR of reconstructed signal is 12.13 db.
IV.
CONCLUSION
In this paper we used Discrete Wavelet Transform for analysis of speech signal and processed signal up to level of 5 decompositions, filtered the noise with soft thresholding method and obtained nearly perfect signal which has SNR 12.301 db after 5 decomposition levels.
V.
REFERENCES
[1]
Çiğdem Polat Dautov and Mehmet SiraçÖzerdemb “Introduction to Wavelets and their applications in signal denoising”, Bitlis Eren University Journal Of Science And Technology 8(1) (2018).
[2]
TIE Yong and Wang Qiang, “The Realization of Wavelet Threshold Noise Filtering Algorithm in DSP”, 2010 International Conference on Measuring Technology and Mechatronics Automation.
[3]
https://en.wikipedia.org/wiki/Wavelet
[4]
RobiPolikar, https://web.iitd.ac.in/~sumeet/WaveletTutorial.pdf
[5]
Andrew Dlugan, http://sixminutes.dlugan.com/speech-evaluation-1-how-to-study-critique-speech/
[6]
Lawrence R. Rabiner and Ronald W. Schafer, “Introduction to Digital Speech Processing”, NOW the essence of knowledge(2007)
[7]
Steven W. Smith,” Digital Signal Processing ”, Chapter 22.
[8]
Martin Welk, Achim Bergmeister, and Joachim Weickert, “Denoising of Audio Data by Nonlinear Diffusion”, https://www.mia.uni-saarland.de/Publications/welk-bw-ss05.pdf
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