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   -> Volume 6, Issue 3

Preprint: Filter banks over commutative rings
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Andreas Klappenecker (

PostPosted: Wed Feb 19, 1997 4:25 pm    
Subject: Preprint: Filter banks over commutative rings
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#4 Preprint: Filter banks over commutative rings

A new preprint is available:

Title: Two-Channel Perfect Reconstruction Filter Banks over Commutative Rings
Authors: Andreas Klappenecker, Matthias Holschneider, and Kristin Flornes

Abstract: We develop a theory of perfect reconstructing filter banks
over commutative rings $A$ with identity. The filter bank viewpoint is
complemented by interpreting the signals as elements of the free
$A$-module of finitely supported sequences with values in $A.$ It is
shown that bases of this module can be obtained by the even translates
of the synthesis filter sequences of a perfect reconstructing filter
bank. We associate a group structure with these bases and thereby
obtain a parametrization of synthesis filter pairs. It is proved that
this parametrization is complete, provided that $A$ is an arbitrary
field. As a special case we derive a complete parametrization of
biorthogonal real-valued filter pairs. We discuss lifting techniques
and their use to reduce the computational complexity of

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Andreas Klappenecker
Universitaet Karlsruhe
D-76128 Karlsruhe
All times are GMT + 1 Hour
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