Performance analysis of wavelet transform-based adaptive filtering

The wavelet transform has been introduced for quite some time now. We examine the performance of wavelet transform-based adaptive filters. The application of two typical wavelets (D4 and Haar wavelets) are studied extensively as indicators of wavelet transform-based adaptive filter performance in general. Experimental results for a system identification application show an improvement in signal modelling and satisfactory convergence speed for a variety of equalisation conditions. We also compare the wavelet transform-based adaptive filters of Lee and Un (1986) to other transform-based adaptive filters such as discrete-cosine transform (DCT), discrete sine transform (DST), discrete Fourier transform (DFT), Walsh Hadamard transform (WHT) and discrete Hartley transform (DHT). The results of this comparison are mixed. We find that the performance depends on many factors but are consistent with the findings of Lee and Un. The results are also largely dependent on the properties of wavelets which have been found to be well suited for analyzing non-stationary signals. Finally, we present computational complexity considerations between these various transform-domain adaptive filters