Pyramidal Riesz products associated with subband coding and self-similarity

John J. Benedetto; Erica G. Bernstein

doi:10.1117/12.205389

6 April 1995 Pyramidal Riesz products associated with subband coding and self-similarity

John J. Benedetto, Erica G. Bernstein

Proceedings Volume 2491, Wavelet Applications II; (1995) https://doi.org/10.1117/12.205389
Event: SPIE's 1995 Symposium on OE/Aerospace Sensing and Dual Use Photonics, 1995, Orlando, FL, United States

Abstract

A new Riesz product is formulated in terms of waveletpacket pyramidal tree structures. A path within such a structure is determined by a lacunarity criterion and a sequence (H_(epsilon (j))) of filters, where each H_(epsilon (j)) is one or the other element of a prescribed subband coding pair (H₀, H₁) of FIR filters. The Riesz product associated with a given path is a continuous radon measure. Path based criteria are given to determine singular and absolutely continuous pairs of such measures. The measures have full support, and their approximants exhibit fractal behavior. These properties can be used to design a secure transmission scheme in communications theory.

Citation Download Citation

John J. Benedetto and Erica G. Bernstein "Pyramidal Riesz products associated with subband coding and self-similarity", Proc. SPIE 2491, Wavelet Applications II, (6 April 1995); https://doi.org/10.1117/12.205389

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