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   -> Volume 6, Issue 8

Answer: Question on M-band wavelets (WD 6.7 #20)
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Author Message (Peter Heller)

PostPosted: Thu Jul 31, 1997 4:50 pm    
Subject: Answer: Question on M-band wavelets (WD 6.7 #20)
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#18 Answer: Question on M-band wavelets (WD 6.7 #20)

There are a number of useful references and software packages for
M-band wavelets. Our group at Aware has published a number of papers
in the EE and applied math literature; preprints can be found on our
ftp site via anonymous ftp, in the directory
/pub/papers/heller. Closed-form expressions and algorithms for
constructing M-band wavelets can be found in the paper

P. N. Heller,
{em Rank $M$ Wavelet Matrices with $N$ Vanishing Moments,}
SIAM J. Matrix Analysis, 16 (1995), pp. 502-518.

Useful earlier papers include:

P. Steffen, P. N. Heller, R. A. Gopinath, C. S. Burrus,
{em Theory of regular $M$-band wavelets,} IEEE Trans. on Signal Processing,
41 (1993), pp. 3497-3511.

G. Welland and M. Lundberg,
{em Construction of compact $p$-wavelets},
Constructive Approximation, 9 (1993), pp. 347--370.

H. Zou and A. H. Tewfik,
{em Discrete orthogonal M-band wavelet decompositions}, in
Proc. IEEE ICASSP-San Francisco, March 1992.

J. Kautsky and R. Turkajova have also done some interesting work at Flinders
U. in Australia on the subject; their work is available via ftp, as mentioned
in an old Wavelet Digest.

Aware, Inc. did at one time offer a software tool named WaveTool for
M-band wavelet design, but unfortunately that software is no longer
available. However, you may find the Rice wavelet toolbox quite
useful in this regard. It was developed by the Computational Math Lab
and DSP group at Rice, and can be found on the web at This is a set of Matlab and C
routines for designing M-band wavelets and performing the
corresponding wavelet transforms and generating sampled
representations of the continuous-time scaling and wavelet functions.
As for applications to image compression, in addition to the Aware
papers available via ftp (e.g. Heller and Resnikoff, ICASSP '93), one
should consult H. Malvar's book {em Signal Processing with Lapped
Transforms}, and the paper

R. L. de Queiroz, T. Q. Nguyen, and K. R. Rao,
{em The GenLOT: generalized linear-phase lapped orthogonal transforms,}
IEEE Trans. on SP, 44 (1996), pp.497-507.

Good luck, I am always happy to answer further questions via email.

Peter Heller
Aware, Inc.
Bedford, MA 01730 USA
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