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   -> Volume 2, Issue 8


Survey of wavelet routines in MATLAB
 
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Marten D. van der Laan, University of Groningen, The Netherlands
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PostPosted: Fri Nov 29, 2002 3:30 pm    
Subject: Survey of wavelet routines in MATLAB
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Survey of wavelet routines in MATLAB

SURVEY of wavelet routines in MATLAB

Via Usenet-News I asked for Matlab-routines for wavelet analysis. I got some
responses which are, in my opinion, interesting for the digest-readers:

#1 From: Serge J. Belongie (sergeb@cco.caltech.edu)

I have put together and debugged some m-files to implement
the forward and inverse DWT with DAUB4 coefficients. The
input data has to be a power of 2. The 1-D version seems
to be working fine, though the 2-D version still has some minor
problems to be worked out. These m-files are very elementary
as far as wavelet analysis goes, and are most likely a tiny
subset of the toolbox you used, but I thought I'd mention it
to you anyway since they are a simple introduction to a really
neat concept.

#2 From: Srinivas Palavajjhala (srini@wuche2.wustl.edu)

The following are some programs I have written in MATLAB.

wtrans - does wavelet packet decomposition and/or decomp. and
reconstruction at each scale using Daubechies Wavelets and
Coifman Wavelets.

mra - does the multiscale plot.

reconph - is reconstruction of high freq part.

reconpl - is reconstruction of low freq part.

#3 From: Marten van der Laan (marten@cs.rug.nl)

I use a toolbox written by J.C. Kantor (kantor@nd.edu). This toolbox
contains routines for the Fast Wavelet Transform (forward and inverse) using
Daubechies wavelets, a routine for iterating the scaling function phi and
wavelet psi, and routines for signal compression using wavelets. This
toolbox has a full TeX documentation.

I tried to contact the author, but I didn't succeed. Anyone who is
interested can contact me.

Myself, I wrote some routines for plotting the wavelet-transformed data in the
time-frequency plane. These routines require Matlab 4.0! I'm currently
fixing some bugs and improving some other things. Again, if you are
interested, contact me.

#4 From: Neil Getz (getz@robotics.Berkeley.EDU)

Neil has written a paper:
"A Fast Discrete Periodic Wavelet Transform"
Memorandum N0. UCB/ERL M92/138

Abstract:
We extend the discrete wavelet transform (DWT) to functions on
the discrete circle to create a fast and complete discrete periodic
wavelet transform (DPWT) for bounded periodic sequences. In so doing
we also solve the problem of non-invertibility that arises in the
application of the DWT to finite dimensional sequences as well as provide
the proper theoretical setting for previous incomplete solutions to the
invertibility problem. We show how and prove that the same filter
coefficients used with the DWT to create orthonormal wavelets on compact
support in l^inf(Z) may be incorporated through the DPWT to create an
orthonormal basis of discrete periodic wavelets. By exploiting transform
symmetry and periodicity we arrive at easily implementable, fast, and
recursive synthesis and analysis algorithms. We include Matlab functions
for DPWT experimentation.

This paper includes MATLAB routines. Please contact the author.

NOTE

I compared the different implementations 1D-discrete wavelet transforms
by Belongie (#1), Kantor (#3) and Getz (#4). Except for some differences in
the lowest frequency components the transformed data were similar.

Also the reconstruction errors (wavelet transform followed by the inverse
wavelet transform) were similar in all three cases.

I only did a very small test with sine input and white noise input, 512
samples. Reconstruction error was of order e-14.

If anyone has some related information, please drop me a message.

Marten D. van der Laan Email: marten@cs.rug.nl
Dept. of Computing Science
University of Groningen
P.O. Box 800
9700 AV GRONINGEN
The Netherlands
All times are GMT + 1 Hour
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