Wavelet-based acoustic echo cancellation
Acoustic echo cancellers are necessary for communication systems such as teleconferencing and full-duplex phone in order to reduce echoes which impair the quality of communication. In this paper we are focusing on the discrete wavelet based adaptive filtering. The discrete-time wavelets offer the possibility to view the discrete-time signal and system modeling from a new perspective which opens interesting and important research issues in adaptive filtering, system identification, and time-series analysis. The wavelet transforms, particularly those orthonormal wavelets with finite support, have emerged recently as a new mathematical tool for multi-resolution decomposition of discrete time signal. In this paper, first the conditions which must be satisfied by the analysis and synthesis filters are determined. Then from the perfect reconstruction quadrature mirror filter (PR-QMF) bank and combined with the decomposition theorem, the relation between the discrete wavelet and iterated filters has been established, further more we consider the possibility of having a discrete wavelet transform which is shift-invariant in the sense that the coefficients at the same scale of the original sequence. Finally we derive the LMS algorithm with the wavelet as the bases function of the echo path. We also studied the properties of the optimum adaptive filter coefficients and showed that it is related to some discrete-time wavelet dependent quantities. Simulation shows that it can converge faster than the general LMS algorithm.