Redundant wavelet filter banks on the half-axis with applications to signal denoising with small delays

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 signal denoising, without delay. Nonetheless, in practice some boundary effects occur and thus a small amount of delay is required to reduce them. The theory is implemented on a challenging signal with large noise and sharp transients. Results from the experimental implementation of the proposed algorithm for the denoising of a feedback signal for controlling a three-phase permanent-magnet synchronous brushless DC motor are also presented.