Redundant wavelet processing on the half‐axis with applications to signal denoising with small delays: theory and experiments

A wavelet transform on the negative half real axis is developed using an average‐interpolation scheme. This transform is redundant and can be used to perform causal wavelet processing, such as on‐line signal denoising, without delay. Nonetheless, in practice some boundary effects occur and thus a small amount of delay is required to reduce them. The effect of this delay is studied using a numerical example of a signal with large noise and sharp transients. It is shown that the delay required to obtain acceptable denoising levels is decreased by using the proposed redundant transform instead of a non‐redundant one. We also present results from the experimental implementation of the proposed algorithm for the denoising of a feedback signal during the control of a three‐phase permanent‐magnet synchronous brushless DC motor. Copyright © 2006 John Wiley & Sons, Ltd.