Performance of wavelet transform based adaptive filters

The use of the wavelet transform in transform domain adaptive filtering (WTAF) is analyzed for performance as measured by learning curves. It is shown that the minimum mean squared error improves significantly with the use of the self-orthogonalizing wavelet transform least mean square (WLMS). An exponentially weighted convergence factor is proposed to introduce scale-based variation to the weight update equation. Simulations for learning curves are obtained by using a conventional smooth signal with sinusoidal components as well as a nonsmooth signal recorded in an electrically noisy environment. The latter signal consists of periodic as well as randomly occurring signals from multiple sources.<>