Speech Enhancement Using Combinational Adaptive Filtering Techniques

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1 Speech Enhancement Using Combinational Adaptive Filtering Techniques 1 A. Raghavaraju, 2 Bhavani Thota 1,2 Chebrolu Engineering College (JNTUK), AP, India Abstract Adaptive filter is a primary method to filter speech signals, because it does not need the signal statistical characteristics. In this paper we present various combinational adaptive filtering techniques for denoising the speech signals. Different filter structures are presented to eliminate the diverse forms of noise using various adaptive algorithms, individually as well as in combination. These are convex combinations of Least Mean Square (LMS), Normalized (N) LMS, Variable Step Size (VS) LMS and Variable Step Size Normalized (VSN) LMS, these are known as CCLMS, CCNLMS, CVSLMS, CVSNLMS algorithms respectively. Finally to measure the capability of the proposed implementations Signal to Noise Ratio Improvement (SNRI) is measured. The simulation results show that the performance of the normalized LMS based algorithm is superior to that of the LMS based algorithm in noise reduction. Keywords Adaptive Noise Cancellation, Combinational Filters, Speech Enhancement, LMS Algorithm I. Introduction In real time environment speech signals are corrupted by several forms of noise such as such as competing speakers, background noise, car noise, and also they are subject to distortion caused by communication channels; examples are room reverberation, low-quality microphones, etc. In all such situations extraction of high resolution signals is a key task. In this aspect filtering come in to the picture. Basically filtering techniques are broadly classified as non-adaptive and adaptive filtering techniques. In practical cases the statistical nature of all speech signals is nonstationary; as a result non-adaptive filtering may not be suitable. Speech enhancement improves the signal quality by suppression of noise and reduction of distortion. Speech enhancement has many applications; for example, mobile communications, robust speech recognition, low-quality audio devices, and hearing aids. Many approaches have been reported in the literature to address speech enhancement. In recent years, adaptive filtering has become one of the effective and popular approaches for the speech enhancement. Adaptive filters permit to detect time varying potentials and to track the dynamic variations of the signals. Besides, they modify their behavior according to the input signal. Therefore, they can detect shape variations in the ensemble and thus they can obtain a better signal estimation. The first adaptive noise cancelling system at Stanford University was designed and built in 1965 by two students. Their work was undertaken as part of a term paper project for a course in adaptive systems given by the Electrical Engineering Department. Since1965, adaptive noise cancelling has been successfully applied to a number of applications. Several methods have been reported so far in the literature to enhance the performance of speech processing systems; some of the most important ones are: Wiener filtering, LMS filtering [1], spectral subtraction [2-3], thresholding [4-5]. On the other side, LMS-based adaptive filters have been widely used for speech enhancement [6 8]. In a recent study, however, a steady state convergence analysis for the LMS algorithm with deterministic reference inputs showed that the steady-state weight vector is biased, and thus, the adaptive estimate does not approach the Wiener solution. To handle this drawback another strategy was considered for estimating the coefficients of the linear expansion, namely, the block LMS (BLMS) algorithm [9], in which the coefficient vector is updated only once every occurrence based on a block gradient estimation. A major advantage of the block or the transform domain LMS algorithm is that the input signals are approximately uncorrelated. Recently Jamal Ghasemi et.al [10] proposed a new approach for speech enhancement based on eigenvalue spectral subtraction, in [11] authors describes usefulness of speech coding in voice banking, a new method for voicing detection and pitch estimation. This method is based on the spectral analysis of the speech multi-scale product [12]. small, but the convergence rate will be slow. Thus, the step size provides a tradeoff between the convergence rate and the steadystate MSE of the LMS algorithm. The performance of the LMS algorithm may be improved by making the step size variable rather than fixed. The resultant approach with variable step size is known as variable step size LMS (VSSLMS) algorithm [13]. By utilizing such an approach, both a fast convergence rate and a small steady-state MSE can be obtained. Many VSSLMS algorithms are proposed during recent years [14-17]. In this paper, we considered the problem of noise cancellation in speech signals by effectively modifying and extending the framework of [1] and [21], using combinations of LMS, NLMS, VSSLMS, and Normalized VSSLMS algorithms. For that, we carried out simulations on various real time speech signals contaminated with real noise. The simulation results show that the performances of the VSSLMS based algorithms are comparable with LMS counterpart to eliminate the noise from speech signals. II. Basic Adaptive Filter Structure Fig. 1 shows an adaptive filter with a primary input that is noisy speech signal s 1 with additive noise n 1. While the reference input is noise n 2, which is correlated in some way with n 1. If the filter output is y and the filter error e= (s 1 +n 1 )-y, then e 2 = (s 1 + n 1 ) 2 2y (s 1 + n 1 ) + y 2 = (n 1 y) 2 + s s 1 n 1 2y s 1. (1) Since the signal and noise are uncorrelated, the mean-squared error (MSE) is E[e 2 ]=E[(n 1 y) 2 ]+E[s 12 ] (2) Minimizing the MSE results in a filter error output that is the best least-squares estimate of the signal s 1. The adaptive filter extracts the signal, or eliminates the noise, by iteratively minimizing the MSE between the primary and the reference inputs. Minimizing the MSE results in a filter error output y that is the best leastsquares estimate of the signal s International Journal of Electronics & Communication Technology

2 ISSN : (Online) ISSN : (Print) Fig. 1: Adaptive Filter Structure A. Conventional LMS Algorithms The conventional LMS algorithm is a stochastic implementation of the steepest descent algorithm. It simply replaces the cost function ξ(n) = E[e 2 (n)] by its instantaneous coarse estimate. The error estimation e(n) is e(n) = d(n) w(n) Φ(n) (3) Where Φ(n) is input data sequence. Coefficient updating equation is w(n+1) = w(n) + μ Φ(n) e(n) (4) Where μ is an appropriate step size to be chosen as 0< μ < for the convergence of the algorithm. Normalized LMS (NLMS) algorithm is another class of adaptive algorithm used to train the coefficients the adaptive filter. This algorithm takes into account variation in the signal level at the filter output and selecting the normalized step size parameter that results in a stable as well as fast converging algorithm. The weight update relation for NLMS algorithm is as follows: w(n+1) = w(n) + μ(n) Φ(n) e(n) (5) The variable step can be written as, μ(n) = μ / [p + Φ t (n) Φ(n)] (6) Here μ is fixed convergence factor to control maladjustment, μ(n) is nonlinear variable of input signal, which changes along with p. The step diminishes and accelerates convergence process. The parameter p is set to avoid denominator being too small and step size parameter too big. The advantage of the NLMS algorithm is that the step size can be chosen independent of the input signal power and the number of tap weights. Hence the NLMS algorithm has a convergence rate and a steady state error better than LMS algorithm. In practical application of the LMS algorithm, a key parameter is the step size. As is well known, if the step size is large, the convergence rate of the LMS algorithm will be rapid, but the steady-state Mean Square Error (MSE) will increase. On the other hand, if the step size is small, the steady state MSE will be small, but the convergence rate will be slow. Thus, the step size provides a tradeoff between the convergence rate and the steadystate MSE of the LMS algorithm. An intuitive way to improve the performance of the LMS algorithm is to make the step size variable rather than fixed, that is, choose large step size values during the initial convergence of the LMS algorithm, and use small step size values when the system is close to its steady state, which results in Variable Step Size LMS (VSSLMS) algorithms. By utilizing such an approach, both a fast convergence rate and a small steady-state MSE can be obtained. By using this approach various forms of VSSLMS algorithms are implemented. Similar to in the case of the LMS algorithm, a variable step size algorithm is also necessary to obtain both fast convergence rate and small steady state MSE. IJECT Vo l. 5, Is s u e Sp l - 3, Ja n - Ma r c h 2014 B. Combinational Adaptive Algorithms So far many algorithms are proposed based on adaptive filters for speech enhancement. The Speech enhancement employs adaptive filters as an integral part of it. There are many types of adaptive filters employing different schemes to adjust the filter weights based on many different criteria. It is fair to say that the LMS algorithm is the most common algorithm used. To improve the performance of LMS-based algorithm, transfer domain LMS adaptive filters are widely used for this application. Other adaptive algorithms such as RLS are used for speech enhancement too. Combination approaches are an effective way to improve the performance of adaptive filters. In the behavior of one such approach has been analyzed. Especially it is shown that its universality performs at least as well as the best of its components. Furthermore, when the component filters satisfy certain conditions. their combination outperforms both of them. In this project, we implement several algorithms in combinational manner for speech enhancement. Here we consider convex combinational LMS (CCLMS), convex combinational normalized LMS (CCNLMS), convex combinational variable step size LMS (CVSLMS), convex combinational variable step size normalized LMS (CVSNLMS). The block diagram of adaptive convex combination of two transversal filters is depicted in fig. 2. The output of the parallel filter is y(n) λ(n) y 1 (n) _[1λ(n)]y 2 (n) (7) Where y 1 (n) and y 2 (n) are the output of two parallel transversal filters at time n. We have i= 1, 2 (8) In (7), λ(n) is the mixing parameter limited between 0 and 1, which is modified via an auxiliary variable a(n). The mixing parameter is defined as λ(n)=sgm[a(n)] (9) Where sgm ( ) is the sigmoid function which is plotted in fig. 2 and defined as sgm[a(n)] = 1 (10) It is shown in [23] that if λ (n) is chosen properly at each iteration, then the above combination would extract the best specifications of the individual filters w 1 (n) and w 2 (n) Fig. 2: Adaptive Convex Combination of Two Transversal Filters International Journal of Electronics & Communication Technology 117

3 The update equation for a(n) is given by (11) The a priori error of the parallel scheme can be expressed as (12) It is possible to improve the tracking performance of the mixing coefficient to manage the step-sizes of the component LMS filter. 1. If λ (n) > β, where β is a threshold close to one, the step-sizes of both filters are multiplied by r. 2. If λ (n) < 1 β, the values of both step-sizes are divided by r, accordingly [22]. Parameter guarantees the stability of the filter, when w 0 changes very fast. In the same fashion various combinations are implemented and tested. These are convex combinational LMS (CCLMS), convex combinational normalized LMS (CCNLMS), convex combinational variable step size LMS (CVSLMS), convex combinational variable step size normalized LMS (CVSNLMS).The performance of these algorithms compared from the convergence characteristics shown in fig. 3. From the convergence curves it is clear that the performance of the CVSNLMS filter is faster than the other combinations and conventional LMS algorithm. The convergence characteristics and MSE for various algorithms are shown in fig. 3 and fig. 4. From the two figures it is clear that CVSNLMS has better performance in terms of convergence rate and MSE. III. Simulation Results To show that combinational algorithms are appropriate for speech enhancement we have used real speech signals and real noisy signals. In all figures number of samples is taken on x-axis and amplitude is taken on y-axis. We considered three scenarios, i.e., speech signal contaminated by helicopter noise (Sample-I) and speech signal contaminated by high voltage noise (Sample-II) and speech signal contaminated by loud speaker noise (Sample-III). A. Simulation Results for Helicopter Noise As a first step in adaptive noise cancellation application, the speech signal corresponding to sample-i is corrupted with random noise and is given as input signal to the adaptive filter shown in Figure 1. As the reference signal must be somewhat correlated with noise in the input, the random noise signal is given as reference signal. The filtering results are shown in fig. 5 and fig. 6. To evaluate the performance of the algorithms signal-to-noise (SNR) improvement is measured and tabulated in Table 1 for various filter structures (all values are in dbs). Fig. 3: Convergence Behavior of Various Combinations Fig. 5: Typical Filtering Results of Helicopter Noise (a) Real Noisy Signal (b) Recovered Signal Using LMS Algorithm, (c) Recovered Signal Using NLMS Algorithm Fig. 2: MSE Behavior of Various Combinations 118 International Journal of Electronics & Communication Technology

4 ISSN : (Online) ISSN : (Print) IJECT Vo l. 5, Is s u e Sp l - 3, Ja n - Ma r c h 2014 Fig. 8: Typical Filtering Results of High Voltage Noise (a) Recovered Signal Using CCLMS Algorithm, (b) Recovered Signal Using CCNLMS Algorithm, (c) Recovered Signal Using CVLMS Algorithm, (d) Recovered Signal Using CVNLMS Algorithm Fig. 6: Typical Filtering Results of Helicopter Noise (a) Recovered Signal Using CCLMS Algorithm,(b) Recovered Signal Using CCNLMS Algorithm, (c) Recovered Signal Using CVLMS Algorithm, (d) Recovered Signal Using CVNLMS Algorithm Fig. 7: Typical Filtering Results of High Voltage Noise (a) Real Noisy Signal (b) Recovered Signal Using LMS Algorithm, (c) Recovered Signal Using NLMS Algorithm B. Adaptive Cancellation of Real High Voltage Murmuring In this experiment a speech signal corresponding to sample-ii contaminated with high voltage murmuring is given as in put to the filter. The filtering results are shown in fig. 7 and fig. 8. IV. Conclusion In this paper the problem of noise removal from speech signals using convex combination based adaptive filtering is presented. For this, the same formats for representing the data as well as the filter coefficients as used for the LMS algorithm were chosen. As a result, the steps related to the filtering remains unchanged. The proposed treatment, however exploits the modifications in the weight update formula for all categories to its advantage and thus pushes up the speed over the respective LMS-based realizations. Our simulations, combinational algorithms is better than conventional LMS and NLMS algorithms in terms of SNR improvement and convergence rate. Hence these algorithms are acceptable for all practical purposes. References [1] B. Widrow, J. Glover, J. M. McCool, J. Kaunitz, C. S. Williams, R. H.Hearn, J. R. Zeidler, E. Dong, R. Goodlin, Adaptive noise cancelling: Principles and applications, Proc. IEEE, Vol. 63, pp , Dec [2] B. L. Sim, Y. C. Tong, J. S. Chang, C. T. Tan, A parametric formulation of the generalized spectral subtraction method, IEEE Trans. On Speech and Audio Processing, Vol. 6, pp , [3] I. Y. Soon, S. N. Koh, C. K. Yeo, Noisy speech enhancement using discrete cosine transform, Speech Communication, Vol. 24, pp , [4] H. Sheikhzadeh, H. R. Abutalebi, An improved waveletbased speech enhancement system, Proc. of the Eurospeech, [5] S. Salahuddin, S. Z. Al Islam, M. K. Hasan, M. R. Khan, Soft thresholding for DCT speech enhancement, Electron. Letters, Vol. 38, No. 24, pp , [6] J. Homer, Quantifying the convergence speed of LMS adaptive filter with autoregressive inputs, Electronics Letters, Vol. 36, No. 6, pp , March [7] H. C. Y. Gu, K. Tang, W. Du, Modifier formulaon mean square convergence of LMS". [8] Jamal Ghasemi, Mohammad Reza Karami Mollaei, A New Approach for Speech Enhancement Based On Eigenvalue Spectral Subtraction, Signal Processing: An International Journal, Vol. 3, Issue. 4, pp [9] M. Chakraborty, H. Sakai, Convergence analysis of a complex LMS algorithm with tonal reference signals, IEEE Trans. on Speech and Audio Processing, Vol. 13, No. 2, pp , March [10] S. Olmos, L. Sornmo, P. Laguna,"Block adaptive filter with deterministic reference inputs for event-related signals: International Journal of Electronics & Communication Technology 119

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