# Speech Enhancement in Presence of Noise using Spectral Subtraction and Wiener Filter

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2 comes from its minimal complexity and low computational load. In this method the speech spectrum enhanced by subtracting an average noise spectrum from the noisy speech spectrum. Here it is assumed that, noise is uncorrelated and additive to the noise. II. Spectral Subtraction Method It is based on the basic principal of restoring the signal by subtracting an estimate of the noise spectrum from the noisy speech spectrum. The noise spectrum can be estimated from the pauses and quite periods in the speech signal. When there is no speech being said and only noise is present. Basic assumption is noise is additive. Spectral subtraction of the signal takes place in the frequency domain. The data from the signal are segmented and windowed by using Hamming window followed by FFT to transform the signal from time domain to frequency domain. Let p(k) and n(k) be represented by a windowed speech signal and noise signal respectively. The sum of the two is then denoted by x(k), x(k) = p(k) + n(k). (1) Where x(k), p(k) and n(k) are the noisy signal, the original signal and the noise respectively. By applying Fourier transform on both sides of equation (1). X(e jw )=P( e jw ) + N (e jw ) (2) X w (w) 2 = P w (w) 2 + N w (w) 2 + P w (w).n w (w) * + P w (w) *.N w (w) (5) If we assume the noise component n(k) is un- correlated to p(n). Then the terms P w (w).n w (w) * and P w (w) *.N w (w) are reduced to zero. From the above based assumptions the estimation of clean speech can be estimated as follows P w (w) 2 = X w (w) 2 - N w (w) 2 (6) A more general form can be derived by generalizing the exponent from 2 to b. P w (w) b = X w (w) b - α N w (w) b (7) Where b represents the power exponent, for magnitude spectral subtraction, the exponent b=1, and for power spectral subtraction, b=2. The parameter α controls the amount of noise subtracted from the noisy signal. For full noise subtraction α=1, and for over subtraction α>1. III. Algorithm The overview of the algorithm presented in Fig. 1. The input signals are digitized with a sampling rate of 8 KHz. The analysis window is a 128 point Hamming window and the overlap between two successive windows is set to be 50%. In order to avoid wrap around errors each frame is zero padded to 256 point. The frequency transformation of the signal is done by using FFT. Where X(e jw ), P(e jw ) and N(e jw ) are the fourier transforms of the noisy signal, the original signal and the additive noise. Further the incoming signal is x(k) is divided into segments of length N. and each segment is windowed by using a hamming window and then transformation is performed via FFT. The window signal is given as follows x w (m) = w(m) x(m) = w (m) [p(m) + n(m)] =p w (m) + n w (m) (3) The frequency domain representation for the windowed operation can be represented as X w (f)=p w (f) + N w (f) (4) In the frequency domain, with their respective Fourier Transforms, The power spectrum of the noisy signal is given by Fig. 1: Block Diagram of Spectral Subtraction Method Available 180

3 IV. Spectral Subtraction Via Weiner Filtration Weiner filtering was first proposed by Norbert Weiner in This type of filter generally is used to estimate or to predict the signal in presence of noise. For the implementation of the Weiner filter requires the power spectra of the signal and the noise process. The frequency domain representation of the noisy signal, the original signal and the additive white noise is represented by equation (5). The formulation for the Weiner filter is as follows. W ( f ) P XX Pxx ( f ) ( f ) P yy ( f ) (8) Where P xx (f) and Pyy(f) represents the estimated power spectra of the noise free signal and the background noise. Which are assumed to be uncorrelated and stationary. After calculating the transfer function W(f). Dividing equation (8) by P yy (f). SNR( f ) ( f ) SNR( f ) 1 W (9) (car noise, train noise and babble noise) with different signal to noise ratio (10, 5, 0dB). The amount of noise reduction is generally measured with the SNR improvement. Fig. 3. Clean Speech signal (blue), Clean speech signal added with 5 db AWGN (red), and filtered signal (green). Fig. 4. Speech signal with car noise of 0 db (red) and filtered signal (Green) Fig. 2 shows the block diagram of Weiner filter V. Results and Discussions For the evaluation of performance of spectral subtraction and wiener filter, a time spectrum of several utterances in presence of noise is analyzed and to show the improvement of the noisy speech signal, to conduct experiments we have used speech signals constituted by sentences pronounced in English language by male and female speakers. The speech signals are sampled with 8kHz and are corrupted by three types of additive noise Available 181

4 Fig. 5. Speech signal with train noise of 0 db (red) and Fig. 8. Speech signal with car noise of 5 db (red) and Fig. 6. Speech signals with babble noise of 0 db (red) and Fig. 9. Speech signal with car noise of 5 db (red) and Figure [3] to [6] shows the results of spectral subtraction working at SNR of 0 db for noisy speech signal, car noise, train noise and babble noise. From the figures it can be seen that the filter does indeed remove the noise. It shows the magnitude of the speech against time. Figure [7] to [9] shows the results from the wiener filter implementation. From these figures it is clear that the noisy signal has been filtered and up to certain extent noise has been removed. Fig. 7. Speech signal with car noise of 5 db (red) and VI. TESTING The testing method involves the listening of the filtered speech with listeners and examining the results of the filtered signal. The testing results appear to be relatively close in quality of filtered speech for both the methods. Available 182

5 CONCLUSION In this paper, the speech enhancement method by using spectral subtraction and wiener filter had been implemented and analyzed. The methods improve the speech quality by increasing the signal to noise ratio. This method provides a definite improvement compared to other traditional speech enhancement methods. The results from both simulation and evaluation suggest that, this method achieves better reduction of the noise for different noisy signals such as car noise, train noise and babble noise. REFERENCES 1. S. Boll, Suppression of acoustic noise in speech using spectral subtraction, IEEE Transactions on Acoustics, Speech, Signal Processing vol.27, pp , Apr Y. Ephraim and D. Malah, Speech enhancement using a minimum mean-square error short-term spectral amplitude estimator, IEEE Transactions on Acoustics, Speech, Signal Processing vol.assp-32, No.6, pp , Dec Y. M. Cheng and D. O'Shaughnessy, Speech enhancement based conceptually on auditory evidence," IEEE Trans. Signal Processing, vol. 39, Sept Y. Ephraim and H. L. Van Trees, A signal subspace approach for speech enhancement," IEEE Trans. Speech and Audio Processing, vol. 3, July Scalart, P., and Filho, J. Speech enhancement based on a priori signal to noise estimation, in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, pp Md. Kamrul Hasan, Sayeef Salahuddin, and M. Rezwan Khan, A Modified A Priori SNR for Speech Enhancement Using Spectral Subtraction Rules, IEEE Signal Processing Letters, vol. 11, no. 4, April B. L. Sim, Y. C. Tong, J. S. Chang, and C. T. Tan, A parametric formulation of the generalized spectral subtraction method, IEEE Trans. Speech Audio Processing, vol. 6, pp , July Available 183

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