An adaptive filter based on wavelet transform and affine projection algorithm

Based on the wavelet transform (WT) and the affine projection algorithm, a new adaptive filter with a variable step-size scheme, so-called WAPA filter, is proposed in this paper. The computation performance of the WAPA filter is further verified by some numerical simulations and engineering applications. Comparing with the traditional affine projection algorithm (APA), the newly proposed algorithm can provide a faster convergence speed with the same mean square errors (MSE). This implies that the WAPA order may be reduced for a same filtering result; and the saved computation time may counteract the computation expenses of the wavelet transform. The faster convergence speed and the lower steady state MSE (or mis-adjustment) can be attributed to the variable step-size scheme adopted in the WAPA, which is much better than the normal variable step-size APAs.