Discrete-time wavelet transform

Manuel A. Sola; Sebastia Sallent-Ribes

doi:10.1117/12.217634

1 September 1995 Discrete-time wavelet transform

Manuel A. Sola, Sebastia Sallent-Ribes

Proceedings Volume 2569, Wavelet Applications in Signal and Image Processing III; (1995) https://doi.org/10.1117/12.217634
Event: SPIE's 1995 International Symposium on Optical Science, Engineering, and Instrumentation, 1995, San Diego, CA, United States

Abstract

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.

Citation Download Citation

Manuel A. Sola and Sebastia Sallent-Ribes "Discrete-time wavelet transform", Proc. SPIE 2569, Wavelet Applications in Signal and Image Processing III, (1 September 1995); https://doi.org/10.1117/12.217634

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KEYWORDS

Transform theory

Wavelets

Wavelet transforms

Filtering (signal processing)

Radon

Digital filtering

Digital signal processing

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