IMPROVED NOISE CANCELLATION IN DISCRETE COSINE TRANSFORM DOMAIN USING ADAPTIVE BLOCK LMS FILTER

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1 SANJAY KUMAR GUPTA* et al. ISSN: [IJESAT] INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE & ADVANCED TECHNOLOGY Volume-, Issue-3, IMPROVED NOISE CANCELLATION IN DISCRETE COSINE TRANSFORM DOMAIN USING ADAPTIVE LOCK LMS FILTER Sanjay Kumar Gupta, Jitendra Jain, Rahul Pachauri 3 Student (M.Tech.), Electronics & Communication, Jaypee University o Engineering & Technology, Madhya Pradesh, India, sanjay.newage3@gmail.com Student (M.Tech.), Electronics & Communication, Jaypee University o Engineering & Technology, Madhya Pradesh, India, jitendrajn69@gmail.com 3 Senior Lecturer, Electronics & Communication, Jaypee University o Engineering & Technology, Madhya Pradesh, India, rahul.pachauri@juet.ac.in Abstract This paper illustrates the advantages o Discrete Cosine Transorm (DCT) when it is used in lock least mean square (LMS) adaptive ilter. DCT provides very good energy compaction in speech signals, image signals. So the signal to noise (SNR) is improved. Noise cancellation, Echo cancellation, System identiication are the application o adaptive ilter. We have proposed the Noise cancellation in DCT Domain and also compare with exist Fast lock LMS (FLMS). The simulation result shows better signal to noise ratio (SNR) in DCT Domain rather than FFT Domain. Index Terms: Fast lock LMS (FLMS), Least Mean Square (LMS) algorithm, DCT *** INTRODUCTION It is oten necessary to perorm speech enhancement through removal o noise rom speech processing system operating in noisy environment. The noise degrades the perormance o speech and voice recognition system. There are certain applications o signal processing that require adaptive ilters the length o which exceed a ew hundred or even a ew thousand taps. In the application o speech processing in which the noise coming with speech signal, channel equalization and echo cancellation may require adaptive ilter with exceedingly long lengths. For these application LMS algorithm is computationally expensive to implement. ecause ilter weight is changed or each sample so it requires more time to be processed. So lock processing o data samples signiicantly reduces the computational complexity o adaptive ilters. In lock processing, a block o samples o the ilter and desired output are collected and then processed together to obtain a block o output samples and ilter weight is changed or each block. And when we do it in requency domain this is called FLMS. The topic Noise cancellation and many speech enhancements is widely researched and many speech algorithms make use o FFT to make it easier to remove noise embedded in the noisy speech signal. In transorm domain it is easy to separate the speech energy and noise energy or example energy o white noise is uniormly spread through the entire spectrum, but the energy o speech, concentrated in certain requencies. We have proposed the block LMS (LMS) algorithm in discrete cosine transorm domain or noise cancellation in speech processing. DCT is most avourable or the compression o speech and image data. This is very useul in speech iltering, data compression and eature extraction. When the colored noise is mixed with speech or the signal is highly correlated then DCT exactly de-correlate the signal. DCT output consists o signal components separated in to individual requency bands. DCT exhibits excellent energy compaction or highly correlated signals. The uncorrelated signal has its energy spread out, whereas the energy o the correlated image is packed into the low requency region. It will be shown in this paper how DCT perorm well as well as FFT. This improvement helps to reduce the residual noise present, which is musical in nature.. DCT DCT is widely used in image compression because o its excellent energy compaction property. This is a useul eature or noise removal purpose too. I the speech energy can be concentrated predominantly into a ew coeicients while the noise energy remains white, reduction o noise can be achieved easily. As it was shown in previous work on speech IJESAT May-Jun 0 Available 498

2 SANJAY KUMAR GUPTA* et al. ISSN: [IJESAT] INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE & ADVANCED TECHNOLOGY Volume-, Issue-3, coding [,7], DCT provides signiicantly higher energy compaction as compared to the FFT. DCT has the added advantage o higher spectral resolution than the FFT or the same window size. For a window size o N, the DCT has N independent spectral components while the FFT only produces N/ + independent spectral component, as the other components are just complex conjugates. This is yet another point in avor o the use o the DCT. FFT only attempt to correct the noisy amplitude but not the phase component. This actually results in an upper bound on the imum improvement in SNR possible. I DCT is used, a higher upper bound is possible. The eect o non-corrected phase on the speech discussed in [5]. I the phase is out by more than π /8, the speech becomes rough. I the phase is replaced by random noise uniormly distributed between -π to π, a rough and completely unvoiced speech is obtained. On the other hand, i the phase is replaced by zero, the reconstructed speech sounds completely voiced and monotonous. Thereore it is not correct to view the phase as totally unimportant and especially or high levels o additive noise; the reconstructed speech quality will be aected. For DCT, the coeicients are real and can be considered to have a binary phase value. The phase will depend only on the sign o the coeicient. This provides a better degree o noise margin as unless the added noise changes the sign o the coeicient, the phase is unchanged. Thereore i strong speech energy is present in a particular coeicient, it is unlikely that the phase will be corrupted. I the noise energy is much higher than the speech energy in a particular coeicient resulting in an erroneous phase, the coeicient will be highly attenuated thus minimizing the eect o the erroneous phase. It is thereore likely that DCT would perorm better than FFT. One dimensional DCT is given as ollows: [,8] Forward transorm o a sequence {x n, 0 n N } is given by, N π n + k () X k = α k x n cos, N Where, n=0 α 0 = N, α k = N 0 k N The inverse Transorm is given by, x n = N k=0 α k X(k) cos or k N π n+ k N 0 k N, () 3. DCT ASED LOCK LMS ADAPTIVE FILTER (DLAF) 3.. Fast lock LMS Algorithm Consider a LMS based adaptive ilter that takes an input sequence x(n), which is portioned into non-overlapping blocks o length P each by means o a serial to parallel converter, and the block o data is so produced are applied to an FIR ilter o length N, one block at a time. The tap weights o the ilter are updated ater the collection o each block o data samples, so that the adaption o the ilter proceeds on a block-by-block basis rather than on a sample by sample basis as in conventional LMS algorithm. [3, 7] (3) W( i ) W( i) [ RW P] L t Where, R x( il r) x ( il r) L L is the lock length, R is the autocorrelation matrix and P, cross correlation vector. The weight update equation is, L W ( i ) W ( i) x( il r) e( il r) L r0 The error vector is, e( il r) d( il r) y( il r) The output is, r0 L P x( il r) d( il r) L r0 y( il r) W t ( i) x( il r) Deine the matrix (kth block), X(i) [X(iL) X(iL )... X(iL L )] T The column Vectors are, d(i) [d(il) d(il )... d(il L )] T y(i) [y(il) y(il )... y(il L )] T e(i) [e(il) e(il )... e(kl L )] T lock Interval 4L Sample Interval 4 Step size should be bounded as, (4) (5) (6) (7) (8) (3) L 0 (9) (0) () () IJESAT May-Jun 0 Available 499

3 SANJAY KUMAR GUPTA* et al. ISSN: [IJESAT] INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE & ADVANCED TECHNOLOGY Volume-, Issue-3, Tap weight adaption: 0 e ( k) DCT ek ( ) w k w k k x k e k * ( ) ( ) ( ) ( ) ( ) Note: N is the ilter length, L is the block length N =N+L- denotes the element by element multiplication σ i is the power estimates o the sample o ilter input in the requency domain. Fig- shows the DLAF Adaptive ilter, [6] 3.. DLAF Algorithm Input: Output: Tap weight vector, w (k) Signal power estimates σ x,f k s Extended input vector, x k = [x(kl N + ).. x(kl + L )] T Desired output vector, d k = [d(kl N + ).. d(kl + L )] T Filter output y k = [y(kl N + ).. y(kl + L )] T. Filtering: x k = DCT(x k ). Error estimation: e(k) = d(k) y(k) 3. Step normalization: Tap weight vector update w (k+) y( k) thelast element o IDCT ( x ( k) w ( k)) ( ) x ( k) xf, i( k ) xf, i( k) F, i ( k) [ 0( k) ( k)... ' ( )] T N k 0 i ( k) F, i( k ) 4. ADAPTIVE NOISE CANCELLATION Separating a signal rom additive noise is a common problem in signal processing. Fig- [4, 6] shows the adaptive noise cancellation technique. This approach is viable only when an additional reerence input is available containing noise n, which is correlated with the original corrupting noise n 0. In igure the adaptive ilter receives the reerence noise, ilter it, and subtract the result rom the noisy primary input, s+n 0. For the adaptive ilter, the noisy input s+n 0 acts as the desired response. The system output acts as the error or the adaptive ilter. One might think that some prior knowledge o the signal s or o the noises n 0 and n would be necessary beore the ilter could adapt to produce the noise-cancelling signal y. A simple argument will show, however, that little or no prior knowledge o s, n 0, or n o their interrelationships is required. Assume that s, n 0, n and y are statistically stationary and have zero means. Assume that s is uncorrelated with n 0 and n and suppose that n is correlated with n 0. That output is [4] ε = s + n 0 y Squaring, one obtains ε = s + (n 0 y) + s(n 0 y) (5) Taking expectation o both sides o equation 4, and realizing that s is uncorrelated with n 0 and with y, yields E ε = E s + E[ n 0 y) + E[s n 0 y ] = E s + E[ n 0 y) (6) Adapting the ilter to minimize E ε will not aect the signal power E s. Accordingly, the minimum output power is E min ε = E s + E min [ n 0 y) (4) (7) IJESAT May-Jun 0 Available 500

4 SANJAY KUMAR GUPTA* et al. ISSN: [IJESAT] INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE & ADVANCED TECHNOLOGY Volume-, Issue-3, When the ilter is adjusted so that E s is minimized, thereore E[ n 0 y), is also minimized. The ilter output y is then best least-squares estimate o the primary noise n 0. Moreover, when E[ n 0 y) is minimized, E[ ε y) is also minimized, since, rom equation 5, In Fig-3, a shows the Speech signal, b shows the engine noise added with speech signal, c shows the FLMS output and d shows the DLAF output with N=6, β=.99. ε s = n 0 y (8) Adjusting or adapting the ilter to minimize the total output power is tantamount to causing the output ε to be a best leastsquare estimate o the signal s or the given structure and adjustability o the adaptive ilter and or the given reerence input. [4] (a) (b) Fig-: Noise Cancellation 5. SIMULATION RESULT In the ollowing simulation, the speech signal and engine noise is recorded. We add both the signals with white noise. We have taken the ilter length like 8, 6, 3, 64, 8 and dierent step size. And it is iltered through FLMS and DLAF and calculates the input and output SNR. From the simulation, we may see the DLAF provide the high SNR. Table shows the comparison o FLMS and DLAF iltering with dierent- step size and ilter length. (c) Table-: Comparison o FLMS and DLAF Output SNR Step Input FLMS DLAF Size SNR N=6 N=3 N=64 N=6 N=3 N= Fig-3: Simulation result: (d) (a) Speech Signal, (b) Signal with engine noise, (c) FLMS Result, (d) DLAF Result IJESAT May-Jun 0 Available 50

5 SANJAY KUMAR GUPTA* et al. ISSN: [IJESAT] INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE & ADVANCED TECHNOLOGY Volume-, Issue-3, CONCLUSION This paper clearly shows the easibility o using DCT or noise cancellation. The use DLAF generates better results as compared to FLMS. The improvement is also more noticeable or engine noise and white noise. Although the algorithm is simulated with the DCT, it should also be applicable to other types o transorm such as the wavelet transorm, Fractional Fourier transorm. REFERENCES [] N. Ahmed, T. Natarajan, K.R. Rao, Discrete cosine transorm, IEEE Trans. Comput. C-3 (974) [] Earl R. Ferrara, "Fast Implementation o LMS Adaptive Filters", IEEE Transactions on acoustics, speech, and signal processing, vol. Assp-8, no. 4, august 980. [3] S.S. Narayan and A.M. Peterson, Frequency domain least mean square algorithm, Proc. IEEE, 69():4-6, January 98. [4] G.A. Clark, S.K. Mitra and S.R. Parker, lock Implementation O Adaptive Digital Filters, IEEE Trans. Circuit Syst., Vol CAS-8, PP , June 98. [5]. Widraw and S.D. Stearns, Adaptive signal Processing, Prentice-Hall, Englewood Clis, NJ, 985. [6] P. Vary, Noise suppression by spectral magnitude estima-tion - Mechanism and theoretical limits, Signal Processing 8 (985) [7] S. Haykin, Adaptive Filter Theory, Englewood Clis, NJ: Prentice-Hall, 986. [8]. Farhang-oroujeny, Adaptive Filters: Theory and Applications,Chichester, Ed. Wiley, 998. [9] Ing Yann Soon, Soo Ngee Koh, Chai Kiat Yeo, Noisy speech enhancement using discrete cosine transorm, ELSEVIER Science, Speech communication 4 (998) [0] D.P. Das, G. Panda and S.M. Kuo, "New block iltered-x LMS algorithms or active noise control systems", IET Signal Process., 007,, (), pp IJESAT May-Jun 0 Available 50