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   -> Volume 5, Issue 1

Preprint: Preprints on wavelet-related research from Aware, Inc.
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Author Message (Peter Heller)

PostPosted: Tue Dec 03, 2002 4:15 pm    
Subject: Preprint: Preprints on wavelet-related research from Aware, Inc.
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Preprint: Preprints on wavelet-related research from Aware, Inc.

Preprints on wavelet-related research from Aware, Inc.

A number of preprints on wavelets and their applications are available in
electronic form (as compressed postscript files) from Aware, Inc.'s ftp site,, via anonymous ftp. The directory pub/papers/heller contains
papers by Peter Heller and collaborators, including the recent preprint:



V. Strela, P. N. Heller, G. Strang, P. Topiwala, C. Heil

submitted to IEEE Transactions on Image Processing, 1995

Multiwavelets are a new addition to the body of wavelet theory.
Realizable as matrix-valued filter banks leading to wavelet bases,
multiwavelets offer simultaneous orthogonality, symmetry, and short
support, which is not possible with scalar 2-channel wavelet systems.
After reviewing this recently developed theory, we examine the use of
multiwavelets in a filter bank setting for discrete-time signal and
image processing. Multiwavelets differ from scalar wavelet systems in
requiring two or more input streams to the multiwavelet filter bank.
We describe two methods (repeated row and
approximation/deapproximation) for obtaining such a vector input
stream from a one-dimensional signal. Algorithms for symmetric
extension of signals at boundaries are then developed, and naturally
integrated with approximation-based preprocessing. We describe an
additional algorithm for multiwavelet processing of two-dimensional
signals, two rows at a time, and develop a new family of multiwavelets
(the constrained pairs) that is well-suited to this approach. This
suite of novel techniques is then applied to two basic signal
processing problems, denoising via wavelet-shrinkage, and data
compression. After developing the approach via model problems in one
dimension, we applied multiwavelet processing to images, frequently
obtaining performance superior to the comparable scalar wavelet

A second directory, pub/papers/sandberg, contains papers by Stuart Sandberg
and coauthors, including:



Stuart D. Sandberg and Michael A. Tzannes

appears in IEEE Journal on Selected Areas in Communications, December, 1995

Multicarrier modulation possesses several
properties which make it an attractive approach for high speed copper
wire communications networks. Among these properties are the ability
to efficiently access and distribute multiplexed data streams, and a
reduced susceptibility to impulsive, as well as to narrowband channel
pdisturbances. In digital implementations of multicarrier modulation,
subcarrier generation and data modulation are accomplished digitally
using orthogonal transformations of data blocks. These
implementations are particularly efficient with regard to bandwidth
utilization and transceiver complexity. In this paper, we present a
form of digital multicarrier modulation which we refer to as
overlapped discrete multitone, or discrete wavelet multitone (DWMT),
modulation. For DWMT modulation, which is based on the application of
$M$-band wavelet filters, the pulses for different data blocks overlap
in time, and are designed to achieve a combination of subchannel
spectral containment and bandwidth efficiency that is fundamentally
better than with other forms of multicarrier modulation. We show
that, as a result of the spectral containment feature, DWMT gives a
high level of robustness with regard to noise environments and channel
variations that are encountered in practice.



S. D. Sandberg, S. Del Marco, K. Jagler, and M. A. Tzannes

appears in IEEE Transactions on Communications, November, 1995.

Conventional detection and demodulation rules are not ideally suited
for use with discrete Fourier transform (DFT) based narrow-band
interference suppression, if the DFT incorporates time-weighting to
localize the interference spectrally. Detection rules which are
adapted to the time-weighting are introduced here and shown to offer
significant improvements in performance, but their implementation is
complex. It is found that if a spectrally-contained orthogonal
transform (SCOT) is employed in place of the windowed DFT however, the
conventional detection rules have a level of performance comparable to
that obtained with DFT based suppression and the adapted rules. In
addition to yielding good interference localization, SCOTs benefit
from the fact that they provide a Karhunen-Loeve like transform for
each component of the observation. The primary focus of the paper is
the application of interference suppression for the detection of the
presence of covert signals; however, it is also demonstrated that SCOT
based suppression is potentially better suited than DFT based
suppression for data demodulation in commercial code-division
multiple-access (CDMA) network overlays.

Peter Heller
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