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   -> Volume 7, Issue 4

Preprint: Empirical Tests for Multi-rate Filter Banks
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Carl Taswell (

PostPosted: Wed Mar 25, 1998 12:43 am    
Subject: Preprint: Empirical Tests for Multi-rate Filter Banks
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#2 Preprint: Empirical Tests for Multi-rate Filter Banks

Title: Empirical Tests for the Evaluation of Multi-rate Filter Bank Parameters

Author: Carl Taswell

Submitted: March 1998 to IEEE TCAS-II

Available: with complete set of
multi-color figures to accompany the preprint (example demonstrated in
figures is 4-band 2-regular orthogonal wavelet filter bank).

Empirical tests are developed for evaluating and characterizing
multi-rate $M$-band filter banks represented as $N imes M$ matrices
of filter coefficients. Each test returns a numerically observed
estimate of a $1 imes M$ row vector of parameters with each parameter
element corresponding to a filter band column vector of the filter
bank matrix. These vector valued parameters can be readily converted
to scalar valued parameters for comparison of given filter banks or
optimization in filter bank design. Tests are defined and demonstrated
for $M$-band reconstruction error and delay, $M$-shift biorthogonality
and orthogonality errors, frequency domain selectivity, time frequency
uncertainty, time domain regularity and moments, and vanishing moment
numbers. These tests constitute the verification component of the
first stage of the hierarchical three stage framework (with filter
bank coefficients, single-level convolutions, and multi-level
transforms) for specification and verification of the reproducibility
of wavelet transform algorithms. Example filter banks tested include
a variety of real and complex orthogonal, biorthogonal, and
nonorthogonal $M$-band systems with $Mgeq 2$. Coefficients for these
filter banks were either generated by computational algorithms or
obtained from published tables. The examples demonstrate the
importance of the methodology in revealing discrepancies between
observed and expected results, and thus, in insuring scientific
reproducibility of results and conclusions.
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