Time-invariant orthonormal wavelet representations

A simple construction of an orthonormal basis starting with a so called 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, always be a suitable representation of a signal, particularly when time (or space) invariance is a required property. The conventional way around this problem is to use a redundant decomposition. In this paper, we address the time invariance problem for orthonor-mal wavelet transforms and propose an extension to wavelet packet decompositions. We show that it is possible to achieve time invari-ance and preserve the orthonormality. We subsequently propose an efficient approach to obtain such a decomposition. We demonstrate the importance of our method by considering some application examples in signal reconstruction and time delay estimation.