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