Discrete-time wavelet transform
Manuel A. Sola, Sebastià Sallent · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1995
In this paper we present a family of orthonormal transforms for functions in l2 in which basis functions have compact support and verify a self-similarity criterion at different resolution levels. First, we define the discrete-time orthogonal wavelet transform, a transform that verifies a set of orthonormality properties on a self-similar discrete multiresolution analysis. We relax the constrains imposed on this transform generalizing the concept of self- similarity and defining the generalized discrete-time orthogonal wavelet transform. In this case, it is possible to obtain different levels of self-similarity and more degrees of freedom in the design of basis functions. Finally, a discrete-time self-similar multi-function transform and a discrete-time multi-wavelet transform are presented, and the criteria that basis functions must verify to become an orthonormal transform are pointed out.