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   -> Volume 3, Issue 16


Preprints and software: What to do at the edges in a subband coder
 
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Cormac Herley (cormac@hplceh.hpl.hp.com)
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PostPosted: Mon Dec 02, 2002 1:25 pm    
Subject: Preprints and software: What to do at the edges in a subband coder
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Preprints and software: What to do at the edges in a subband coder

WHAT TO DO AT THE EDGES IN A SUBBAND CODER

One of the ways of taking care of this problem so that
we can apply a filter bank to arbitrary finite-length
segments, or use time-varying filter bank trees is to
use special filters at the boundary.

A set of Matlab m-files to calculate the boundary filters
for orthogonal filter banks is available by anonymous ftp
to ftp.ctr.columbia.edu in directory
CTR_Research/advent/public/software/matlab.

Boundary filters and time-varying filter banks and wavelet
bases are described in detail in

[1] C. Herley and M. Vetterli, "Orthogonal Time-varying Filter Banks
and Wavelet Packets," IEEE Trans SP, October '94.

Abstract of [1]:
We consider the construction of orthogonal time-varying filter banks.
By examining the time domain description of the two-channel
orthogonal filter bank we find it possible to construct a set
of orthogonal boundary filters, which allow us to apply the filter bank
to one-sided or finite-length signals, without redundancy or distortion.
The method is constructive and complete. There is a whole space of
orthogonal boundary solutions, and there is considerable freedom for
optimization. This may be used to generate subband tree structures
where the tree varies over time, and to change between different
filter sets. We also show that the iteration of discrete-time time-varying
filter banks gives continuous-time bases, just as in the stationary
case. This gives rise to wavelet, or wavelet packet, bases for half-line
and interval regions.


Cormac Herley
Hewlett-Packard Labs, Palo Alto, CA
E-mail: cormac@hplceh.hpl.hp.com
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