# Speech Enhancement Based On Noise Reduction

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2 reference sensor senses background noise as n 1 (n) which is correlated to n 0 (n) in some sense but uncorrelated with s(n). The reference noise input n 1 (n) is filtered by the adaptive filter (by performing convolution with filter weights h(n) ) to produce and adjust the output y(n) as close as possible to n 0 (n) for effective noise cancellation [8]. The filter output y(n) is then subtracted from d(n) to obtain an estimation error e(n). The objective here is to minimize the error signal e(n) by using it to incrementally adjust the filter s weights for the next time instant [8]. The estimation error signal is also known as de-noised signal or noise cancelled speech signal. 2.2 NLMS ALGORITHM The LMS algorithm experiences large convergence time for greater values of µ. NLMS offers to solve this problem by normalizing the weight vector w(n) at instant (n+1) with respect to the squared Euclidean norm of input vector x(n) at instant n. Thus, the step size in this algorithm varies with time [7]. The convergence factor is calculated as equation (4). - Eq. (4) 2.1 LMS ALGORITHM The LMS uses the error signal to calculate the filter coefficients and hence one of the simplest algorithms [9]. The output y(n) of the adaptive filter is calculated from the equation (1) The estimation error is calculated by equation (2). - Eq. (1) - Eq. (2) The filter weights are updated as per the equation (3) - Eq. (3) w(n) is the current weight value vector, w(n+1) is the next weight value vector and μ is the convergence factor which determines the convergence time of the filter. α is the NLMS adaption constant aimed to optimize the convergence rate of the algorithm. Preferably, 0< α <2 C is the constant and is always less than 1. The Filter weights are updated as shown in equation (5). 2.3 RLS algorithm - Eq. (5) The RLS algorithm performs the best in time varying environments but at the cost of an increased computational complexity and some stability problems. In this algorithm the filter tap weight vector is updated using equation (6). - Eq. (6) where, intermediate gain vectors used to compute tap weights are calculated as equation (7) & (8), Eq. (7) Eq. (8) λ is a small positive constant < 1. The filter output is calculated using the filter tap weights of previous iteration and the current input vector as shown by the Eq. (9) Eq. (10)

3 2.4 LPC Algorithm LPC algorithm views speech y(z) as an excitation signal e(z) filters with vocal track h(z). Where LPC coefficient can be expressed as p(z),the relationships between e(z), h(z), p(z), y(z) are shown in the figure (3). Shown below are the performance results of all 4 algorithms against a mixed signal wherein ocean sound was used as the background noise for the clean speech signal s(n). (a) Fig 3. Excitation signal filter with LPC Where p(z) can be written as: Eq. (11) (b) (c) Fig.5. Spectrogram of three inputs (a) ocean noise (b) clean speech (c) mixed speech Eq. (12) Eq. (13) (a) (b) Eq. (14) Eq. (15) Here, we replace the excitation signal with our mixed signal, i.e. s(n)+x(n) ( shown in Fig.2). P(z),A(z), and H(z) are obtained from the clean speech s(n). The LPC algorithm was adopted with STFT synthesis and inverse STFT re-synthesis, thus the coefficients were updated frame by frame. 3. Experimental Results To establish the fact that 11 sources of noise used as the database for evaluating the performance of our algorithms are highly diverse and highly uncorrelated, we analyzed their spectrograms (shown in Fig.4). Fig.4. spectrogram of 9 experimented noise environment (c) (d) Fig.6. Spectrogram of noise reduced mixed speech signal (a) LMS (b) NLMS (c) RLS (d) LPC The comparison between run time performances of the 4 algorithms for the above mentioned mixed signal showed LPC to have the highest computation time of sec followed by RLS at sec, NLMS at sec and LMS with lowest of sec. Analysis of spectrograms of the noise reduced mixed signals (Fig.6) indicated another drawback of LPC i.e. though it was able reduce noise in silent portions of the speech, it distorted the perceived audio quality of the noise reduced mixed signal overall. A thorough comparison between LMS, RLS and NLMS algorithms was made for 11 different sources of noise at different values of input SNR and the percentage of correlation between the noise cancelled signal and original clean speech signal was computed (Fig 7). As evident from the data below, RLS restored signal had the highest level of correlation with the original clean speech signal and hence proved to be the best noise cancellation technique. The data for LPC hasn t been shown as it proved to be very inferior in performance and hence its performance statistics were not comparable to the rest 3 algorithms.

4 Case (c): Input SNR = 5 db Case (d): Input SNR = 0 db Fig 7: As seen from table above, the restoration results for noise distorted mixed signal are the best for RLS. Case (a): Input SNR = 15 db 4. Conclusion Case (b): Input SNR = 10 db We observed that for a particular noise source and algorithm, as the SNR decreases the perceived audio quality of the restored signal is better. Further, based on the simulation results, we can deduce the following order of performance for the 4 algorithms, RLS> NLMS > LMS> LPC There is a slight deterioration in performance of LMS for near 0 SNR because of the estimation errors introduced by the noise PSD estimator. However both NLMS and LMS are the most frequently used algorithms for noise reduction and this can be attributed to their low complexity and robustness. Their performance wasn t remarkable for non-stationary environment (i.e. when the noise input exhibits widely varying characteristics with respect to time).the performance can be improved to some extent in such situations by choosing the step size properly. In general, LMS suffered from slow convergence time. The RLS on the other hand, demonstrated the best in nonstationary environments with high convergence time but at the cost of higher complexity.

5 The NLMS algorithm changes the step-size according to the energy of input signals hence it is suitable for both stationary as well as non-stationary environment and its performance lies between LMS and RLS. It provides a trade-off between convergence time and computational complexity. LPC algorithm considers the noise reduction problem from a perceptual and intuitive perspective. However aside from its poor computational performance, the algorithm only cleans out the noise between silent intervals. However, the voiced moment gets distortion effect after filtering the speech from vocal track LPC filter. 5. Future work It has to be noted that since all the algorithms implemented in this paper are basically adaptive in the sense that they need time to analyze noise characteristics in order to filter it out. Consequently they take a few milliseconds to converge before they actually remove the effect of noise from the mixed output signal. This convergence time can pose a serious limitation to these algorithms when the noise in the background is intermittent and has duration shorter than the convergence time of the algorithm. Further, the performance of these algorithms differ with varying sampling rates and for the scenarios where the mixture signal contains more of noise and less of original clean speech signal which motivates for further research in this respect. 6. Acknowledgements The authors would like to thank Professor Zhiyao Duan and also the teaching assistant Xuchen for their extended guidance throughout the research, analysis and documentation process of this paper. 7. References [1]Pascal Scalart et al. Speech Enhancement Based on a priori signal to noise estimation. [2] Kris Hermus et al. A Review of Signal Subspace Speech Enhancement and Its Application to Noise Robust Speech Recognition. [3]Raj Kumar Thenua Simulation And Performance Analysis Of Adaptive Filter In Noise Cancellation. [4] J. Benesty et. al., Adaptive Filtering Algorithms for Stereophonic Acoustic Echo Cancellation. [5] Slock, D.T.M On the convergence behavior of the LMS and the normalized LMS algorithms. [6] Sanaullah khan Comparison of LMS, RLS and Notch Based Adaptive Algorithms for Noise Cancellation of a typical Industrial Workroom. [7] Yuu Seng lau et. al. Performance of Adaptive Filtering Algorithms: A Comparative Study. [8] Bernard Widrow Adaptive Noise Cancelling: Principles and Applications. [9] Udo Zolzer. Digital Audio Effects. [10] James Brain Richardson. LPC-Synthesis Mixture: A Low Computational Cost Speech Enhancement Algorithm. [11] Philipos C. Loizou Speech Enhancement Theory and Practice.

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