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Adaptive Filters in Wavelet Transform Domain

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The paper presents performance comparison between two methods of implementing adaptive filtering algorithms for noise reduction, namely the Normalized time domain Least Mean Squares (NLMS) algorithm, and the Wavelet transform domain LMS (WLMS). A brief theoretical development of both methods is explained, and then both algorithms are implemented on the real time Digital Signal Processing (DSP) system used for audio signals processing. Results are presented showing the performance of each algorithm both in time and frequency domains. Noise reduction effects produced by different algorithms were shown across the spectrum, and distorting effects were analyzed. Trade-offs of convergence speed versus added noise were analyzed. Overall results show convergence speed improvement when using WLMS algorithms over the NLMS algorithm.

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