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

François Chaplais (1) , Panagiotis Tsiotras (2) , Dongwon Jung (2)

1 CAS - Centre Automatique et Systèmes
2 GA TECH - Daniel Guggenheim School of Aerospace Engineering

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.

Domaines: Sciences de l'ingénieur [physics]; Automatique / Robotique

François Chaplais, Panagiotis Tsiotras, Dongwon Jung. Redundant wavelet processing on the half-axis with applications to signal denoising with small delays: Theory and experiments. International Journal on Adaptive Control and Signal Processing, 2006, 20 (9), pp.447 - 474. ⟨10.1002/acs.911⟩. ⟨hal-00501864⟩