TIME-INVARIANT ORTHONORMAL WAVELET REPRESENTATIONS

A simple construction of an orthonormal basis starting with a so-calle d mother wavelet, together with an efficient implementation gained the wavelet decomposition easy acceptance and generated a great research interest in its applications. An orthonormal basis may not, however, a lways be a suitable representation of a signal, particularly when time (or space) invariance is a required property, The conventional way ar ound this problem is to use a redundant decomposition. In this paper, we address the time-invariance problem for orthonormal wavelet transfo rms and propose an extension to wavelet packet decompositions, We show that it is possible to achieve time invariance and preserve the ortho normality, We subsequently propose an efficient approach to obtain suc h a decomposition. We demonstrate the importance of our method by cons idering some application examples in signal reconstruction and time de lay estimation.