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   -> Volume 3, Issue 18


Preprints: Cormac Herley, Hewlett-Packard Labs
 
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Cormac Herley (cormac@hplceh.hpl.hp.com)
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PostPosted: Mon Dec 02, 2002 1:28 pm    
Subject: Preprints: Cormac Herley, Hewlett-Packard Labs
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Preprints: Cormac Herley, Hewlett-Packard Labs

Preprints available:

Two forthcoming papers are available by anonymous ftp to
ftp.ctr.columbia.edu in directory CTR-Research/advent/public/papers/93

"Boundary Filters for Finite-Length Signals and Time-Varying
Filter Banks"

Cormac Herley, Hewlett-Packard Labs

File: her93d.ps.Z

Abstract:
We examine the question of how to construct time-varying filter banks
in the most general $M$-channel non-orthogonal case. We show that by
associating with both analysis and synthesis operators a set of
boundary filters, it is possible to make the analysis structure vary
arbitrarily in time, and yet reconstruct the input with a similarly
time-varying synthesis section. There is no redundancy or distortion
introduced. This gives a solution to the problem of applying filter
banks to finite length signals; it suffices to apply the boundary filters
at the beginning and end of the signal segment. This also allows the
construction of orthogonal and non-orthogonal bases with essentially any
prescribed time and frequency localization, but which, nonetheless, are
based on structures with efficient filter bank implementations.

"Exact Interpolation and Iterative Subdivision Schemes"

Cormac Herley, Hewlett-Packard Labs

File: her93f.ps.Z

Abstract:
In this paper we examine the circumstances under which a discrete-time
signal can be exactly interpolated given only every $M$-th sample.
After pointing out the connection
between designing an $M$-fold interpolator and the construction of an
$M$-channel perfect reconstruction filter bank, we derive
necessary and sufficient conditions on the signal under which exact
interpolation is possible. Bandlimited signals are one obvious example,
but numerous others exist. We examine these and show how the interpolators
may be constructed.

A main application is to iterative interpolation
schemes, used for the efficient generation of smooth curves. We show that
conventional bandlimited interpolators are not suitable in this context.
We illustrate that a better criterion is to use interpolators that
are exact for polynomial functions.
Further, we demonstrate
that these interpolators converge when iterated.
We show how these may be designed for any
polynomial degree $N$ and any interpolation factor $M$.
This makes it possible to design interpolators for iterative
schemes
to make best use of the resolution available in a given display medium.

Cormac Herley
Hewlett-Packard Labs
Palo Alto, CA

E-mail: cormac@hpl.hp.com
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