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   -> Volume 7, Issue 5


Preprint: Unifying Algorithm for Daubechies Wavelets Collection
 
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Carl Taswell (taswell@toolsmiths.com)
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PostPosted: Fri May 08, 1998 8:31 pm    
Subject: Preprint: Unifying Algorithm for Daubechies Wavelets Collection
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#8 Preprint: Unifying Algorithm for Daubechies Wavelets Collection

Title: A Spectral-Factorization Combinatorial-Search Algorithm
Unifying the Systematized Collection of Daubechies Wavelets

Author: Carl Taswell

In press: Invited Paper and Session Keynote Lecture, Intl Conf on
Systems, Signals, Control, Computers to be held Durban South Africa,
September 1998.

Available: www.toolsmiths.com/papers.shtml

Abstract: A spectral-factorization combinatorial-search algorithm has
been developed for unifying a systematized collection of Daubechies
minimum length maximum flatness wavelet filters optimized for a
diverse assortment of criteria. This systematized collection comprises
real and complex orthogonal and biorthogonal wavelets in families
within which the filters are indexed by the number of roots at
$z=-1$. The main algorithm incorporates spectral factorization of the
Daubechies polynomial with a combinatorial search of spectral factor
root sets indexed by binary codes. The selected spectral factors are
found by optimizing the desired criterion characterizing either the
filter roots or coefficients. Daubechies wavelet filter families have
been systematized to include those optimized for time domain
regularity, frequency domain selectivity, time frequency uncertainty,
and phase nonlinearity. The latter criterion permits construction of
the orthogonal least and most asymmetric real and least and most
symmetric complex filters. Biorthogonal symmetric spline and balanced
length filters with linear phase are also computable by these methods.
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