Wavelet transform based adaptive filters: analysis and new results

In this paper the wavelet transform is used in an adaptive filtering structure. The coefficients of the adaptive filter are updated by the help of the least mean square (LMS) algorithm. First, the wavelet transform based adaptive filter (WTAF) is described and it is analyzed for its Wiener optimal solution. Then the performance of the WTAF is studied by the help of learning curves for three different convergence factors: (1) constant convergence factor, (2) time-varying convergence factor, and (3) exponentially weighted convergence factor. The exponentially weighted convergence factor is proposed to introduce scale-based variation to the weight update equation. It is shown for two different sets of data that the rate of convergence increases significantly for all three WTAF structures as compared to that of time-domain LMS. The high convergence rates of the WTAF give us reason to expect that it will perform well in tracking rapid changes in a signal.