Multirate Algorithm for Acoustic Echo Cancellation

Transcription

1 Technology Volume 1, Issue 2, October-December, 2013, pp , IASTER Online: , Print: Multirate Algorithm for Acoustic Echo Cancellation 1 Ch. Babjiprasad, 2 D. Venkata Ramana 3 D.Y.V. Prasad and 4 D. Suresh Asst. Professors,GMR Institute of Technology, Rajam, Srikakulam, A.P., India ABSTRACT The optimum algorithm for updating the coefficients of adaptive filter is LMS algorithm. The method of LMS algorithm gives the optimum error, but it requires more number of computations, because LMS algorithm updates the coefficients for every sample. In this project a new algorithm called multirate algorithm is proposed to reduce the number of computations. This multirate algorithm changes the update rate of the coefficients of the adaptive filter dynamically by analyzing the actual application environment. This algorithm builds a non linear relationship between the update rate and the minimum error. Change in update rate is based on time partition method, which updates the coefficients for every m samples, where m is down sampling rate. If the coefficients are updated for every two samples, it results reduction in computations by half, further increase of down sampling rate reduces more number of computations, but the convergence time increases. To minimize the convergence time, the update rate can be adjusted dynamically by using the relation between down sampling factor and error, in this method. The performance of multirate algorithm is tested by taking an Acoustic Echo Cancellation application, since it required good convergence and tracking properties without posing additional computations. To compare the performance of multirate algorithm, the same application is tested by using LMS algorithm. The method of multirate algorithm gives less number of computations without disturbing convergence time and optimum error when compared to LMS algorithm. Keywords: Adaptive filter, LMS Algorithm. 1. INTRODUCTION A filter is designed and used to extract or enhance the desired information contained in a signal. An adaptive filter is a filter with an associated adaptive algorithm for updating filter coefficients, so that the filter can be operated in an unknown and changing environment. The adaptive algorithm determines filter characteristics by adjusting filter coefficients (or tap weights) according to the signal conditions and performance criteria (or quality Assessment). A typical performance criterion is based on an error signal, which is the Difference between the filter output signal and a given reference (or desired) signal. Fig.1: Basic Functional Blocks of an Adaptive Filter As shown in Fig 1, an adaptive filter is a digital filter with coefficients that are determined and updated by an adaptive algorithm. Therefore, the adaptive algorithm behaves like a human operator that has the ability to adapt in a changing environment. For example, a human operator can avoid a i/p Digital Filter structure (adjustable coefficients) Adaptive algorithm output signal Performanc e criteria Performance Signal Ref 112

2 collision by examining the visual information (Input signal) based on his/her past experience (desired or reference signal) and by using Visual guidance (performance feedback signal) to direct the vehicle to a safe position (Output signal). 2. WIENER FILTER For linear filtering problems with stationary inputs, the adaptive algorithms aim to converge to the same solution as the Wiener filter. This includes applications such as the system identification model considered in this thesis, i.e. echo cancellation, as well as areas such as Signal estimation, prediction and smoothing. Figure 2.2 shows the filtering problem of estimating the excitation or interference process. This is stimulating or corrupting the input signal, having available the original input signal and a reference signal, which is generally known as the desired signal d (n). On due consideration of this filtering problem, produced a Formula for obtaining the optimum solution for the estimated filter taps for a linear Continuous-time filter. This formula required the solution of an integral equation, which has become known as the Wiener-Hopf equation and was based on minimizing the mean square error of the system. The error signal e(n) is the difference between desired signal d(n) and filter response can be expressed as shown in equation 1.3 and the error vector is expressed as e (n)=d(n)-w T (n)u(n) (1) A commonly used criteria for minimization of error function is the minimum mean square error (MSE).which is defined as the expectation of the square error j=e (e 2 (n)) (2) For a given weight vector with stationary input signal x(n) and desired response d(n) the MSE can be calculated as j=e (d 2 (n))-2p T w+w T Rw (3) R = E(x(n)x T (n)) (4) P = E(d(n)x(n)) (5) Where R is the input auto correlation function, P is the cross correlation between input and desired signal. MSE is the quadratic function of the tap weights {w 0, w 1, w 2, w N-1 } The optimum solution can be obtained by taking the first derivative of equation and equate to zero RW 0 =P (6) W 0 =R -1 P (7) Jmin=E (d 2 (n))-p T W 0 (8) Wiener filters minimize the mean square error of the system. This cost function is one of the simplest to mathematically solve and in the majority of cases it has a single global Minimum, particularly in the case of a FIR filter. For the ideal Situation therefore the optimum solution of a Wiener filter exists and can be reached exactly. 113

3 3. MULTIRATE ALGORITHM In LMS algorithm The computational complexity is very high in order to reduce we propose Multirate algorithm, in this the number of computations will reduced nearly a half because of most computation of adaptation algorithm is consumed to update the coefficients vector, the complexity can be reduced almost a half when the coefficients of the adaptive filter is updated only once in every 2 samples this is called factor of 2 down sampling or block filtering of block length of Algorithm 1. initialize m=0, W(0) = 0 and it= max 2. out put Y (n) = x (n)*w t (n) 3. e (n)= d(n)-y(n) 4. W (n+1)=w(n)-2µex (n) 5. m=β 6. n=n+m Adaptive Filtering for Echo Cancellation The best solution for reducing the echo is to use some form of adaptive algorithm. The theory behind such an algorithm and the reasons for choosing that algorithm will be described in this section. Basically filtering is a signal processing technique whose objective is to process a signal in order to manipulate the information contained in the signal. In other words, a filter is a device that maps its input signal into another output signal by extracting only the desired information contained in the input signal. An adaptive filter is necessary when either the fixed specifications are unknown or timeinvariant filters cannot satisfy the specifications. Strictly speaking an adaptive filter is a nonlinear filter since its characteristics are dependent on the input Signal and consequently the homogeneity and additively conditions are not satisfied. Additionally, adaptive filters are time varying since their parameters are continually Changing in order to meet a performance requirement. In a sense, an adaptive filter is a Filter that performs the approximation step on line.the method used to cancel the echo signal is known as adaptive filtering. 4. RESULTS The input signal will be a sinusoidal at 2.0 khz The band limited frequency for telephone transmission is 4 khz. Thus the Nyquist rate is set to eight thousand samples per second. Figure: 4.1 original signal Fig 4.2 generated echo 114

4 Fig 4.3 signal added with echo Fig 4.4: Estimated echo using Adaptive filter The figure 4.4 shows the estimated echo using adaptive filter in which coefficients are updated using multirate algorithm. This is the output of the adaptive filter. Figure: 4.6 Minimum Mean Square Error Echo Canceled Signal Fig 4.7 Characteristics between Error and Down Sampling Rate The figure 4.5 shows the signal which is the output of the echo cancellation system. This signal obtained by subtracting the estimated echo from the signal distorted by ECHO. Minimum Mean Square Error Figure: 4.5 Echo cancellation system output The figure 4.6 shows the minimum mean square error between generated echo and estimated echo. Mean square error convergence to the minimum value after nearly 400 iterations. The time of convergence is =number of samples required to converge/sampling rate. =400/8000=0.05 sec approximately Characteristics between error and down sampling rate: 115

5 Table: 5.1 comparison of number of computations and convergence time in LMS and Multirate algorithm The number of computations in LMS and Multirate algorithm is show in table 5.1 and in multirate algorithm the number of computations reduced by 55% than LMS algorithm, without disturbing the convergence speed. 5. CONCLUSION The project presented a new algorithm for updating the coefficients of adaptive filter; this method keeps a fast update rate at each convergence stage and low computational complexity at the stable stage. The performance of multirate algorithm is tested by taking acoustic echo cancellation as an application. The performance of LMS algorithm is also tested by taking acoustic echo cancellation application. The method of multirate algorithm for updating the coefficients of adaptive filter gives the minimum optimum error, fast convergence and also gives the less number of computations. The performance of the multirate is tested by taking echo cancellation as an application. The echo cancellation using multirate algorithm uses less number of iterations for convergence to optimum solution, because of down sampling rate, the less number of iterations gives the less number of computations, but LMS algorithm uses more number of iterations for convergence to optimum solution. The results of echo cancellation application indicate that the implemented multirate algorithm has the high convergence Speed, low computation complexity, and the same minimum error as the traditional method. 6. REFERENCES Algorithm Number of computatios Convergence time LMS algorithm 64, (approximately) Multirate algorithm 29, [1] Y. Bendel, D. Burshtein, O. Shalvi, Delayless Frequency Domain Acoustic Echo Cancellation, IEEE Transactions on Speech and Audio Processing, 2001, vol. 9, no. 5, pp [2] T. J. Shan, T. Kailath, Adaptive Algorithm with An Automatic Gain Control Feature, IEEE Transactions on Circuits and Systems, 1988, vol.35, no.1, pp [3] J. J. Shynk, Frequency-domain and Multirate Adaptive Filtering, IEEE Signal Processing Mag., 1992, vol. 9, pp [4] G. Clark, S. Mitra, S. Parker, Block Implementation of Adaptive Digital Filters, IEEE Transactions on Circuits and Systems, 1981, vol. CAS-28, pp [5] G. A. Clark, S. R. Parker, S. K. Mitra, A Unified Approach to Time-and frequence-domain Realization of FIR Adaptive Digital Filters, IEEE Transactions on Speech,Audio and Signal Processing, 1983, vol. ASSP-31, pp [6] B. Widrow, Adaptive Filters, In Aspects of Network and System Theory. New York: Hoit, Rinehart and Winson, [7] M. Nekuii, M. Atarodi, A Fast Converging Algorithm for Network Echo Cancellation, Signal Processing Letters,2004, vol. 11, no. 4, pp [8] S. Ohta, Y. Kajikawa, Y. Nomura, Acoustic Echo Cancellation Using Sub-adaptive Filter, International Conference on Acoustics, Speech and Signal Processing, 2007, vol. 1, pp [9] Yao Tian-Ren, Sun Hong. Advanced Digital Signal Processing. Wuhan: HUST Press,