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Wavelet Digest, Vol. 2, Nr. 15.
Wavelet Digest Wednesday, October 20, 1993 Volume 2 : Issue 15
Today's Editor: Wim Sweldens
sweldens@math.scarolina.edu
Today's Topics:
1. Question: matrix multiplication
2. Short course: Wavelets for Engineering Applications.
3. Need help finding wavelet algorithms.
4. Question: Wavelets to divide 2D freq. space in polar coordinates ?
5. Contents: Advances in Computational Mathematics
6. Preprint available
7. Preprints available
8. Reply: Question Coeff. for the Chui wavelets, WD 2.14 # 9.
9. Mathematica wavelet programs available.
10. New Wavelet Toolbox in Matlab
11. Workshop: Wavelets in Chemical Engineering
Submissions for Wavelet Digest:
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Archive site, preprints, references and back issues:
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directories /pub/wavelet and /pub/imi_93.
Gopher and Xmosaic server: bigcheese.math.scarolina.edu.
Current number of subscribers: 2975
--------------------------- Topic #0 -----------------------------------
From: Editor
Subject: Retrieving old issues & new gopher feature
Some problems occurred during the sending of the previous
digest (WD 2.14). Please accept our apologies in case you did not
receive this issue. You can always retrieve it using anonymous ftp
or gopher (cf supra).
Our gopher server also has a new feature that will facilitate searching
through old issues. If you choose the first item from the wavelet
digest information, you will be prompted for a keyword. The server
will then retrieve items (nicely cut out from previous digests)
which are relevant to this keyword. The resulting listing will be
ordered on the basis of keyword frequency and other factors, so
ideally the more relevant articles will appear near the beginning
of the list.
Try it out with keywords such as "fingerprint" or "matlab". Also, more
complex combinations of keywords may provide worthwhile results.
Special thanks go to Brygg Ullmer, a computer science major from the
University of Illinois in Urbana Champaign, who maintains the gopher
server and was able to add this new feature in only a few minutes.
--------------------------- Topic #1 -----------------------------------
From: Jan Pajchel
Subject: Question: matrix multiplication
I should be very much obliged if you could help me with the
following problem:
Consider the computation of a sequence of matrices
Dr=Ar*Br
where Ar,Br are given complex matrices, assumed to be dense and
of large dimension /4094*4096/. They represent the discrete signal
response to an isolated point target in the image.
Can wavelets be used for:
- compression, multiplication and finally decompression ?
- is any software available to try this on real data ?
Sincerely yours:
Jan Pajchel
bray@bg.nho.hydro.com
--------------------------- Topic #2 -----------------------------------
From: Marilyn Grossman, Texas A&M University
Subject: Short course: Wavelets for Engineering Applications.
"Wavelets for Engineering Applications," January 12-15, Texas A&M
University System in College Station, Texas.
Applications-oriented short course featuring Charles K. Chui, author
of the popular book, "An Introduction to Wavelets," and two other
experts of the wavelets research team at Texas A&M University, A.K. Chan
(electrical engineer) and P.K. Yuen (computer scientist). Designed to
build on your basic understanding of wavelet theory, this course will
take you through the concept of time-frequency analysis, the
significance of the integral wavelet transform, and real-time
preprocessing of a continuous signal using cardinal splines. You will
learn how to construct wavelets, how to use decomposition and
reconstruction algorithms, and how to use wavelet packets for frequency
domain fine-tuning in our hands-on laboratory sessions.
409/862-4615 or email: drgrossm@teex.tamu.edu
--------------------------- Topic #3 -----------------------------------
From: Ken Tew <KEN@camp.wpic.pitt.edu>
Subject: Need help finding wavelet algorithms.
In particular I need to get information on wavelet algorithms
that handle large data sets. Currently, the algorithms I've seen
transform an input vector into an equal sized vector of wavelet
coefficients. What I need to have is a matrix of wavelet
coefficients where the columns are wavelet coeffients of sub-vectors of
the input vector. For example, given a vector representing a MINUTE
of data; the output would be a matrix where each column contains the
wavelet coefficients for each SECOND of the input data.
Any books or papers you could recommend on this would be greatly
appreciated.
Thank you. Ken Tew
--------------------------- Topic #4 -----------------------------------
From: zhonglin@mach2.hipl.uci.edu (Zhong-Lin Lu)
Subject: Question: Wavelets to divide 2D freq. space in polar coordinates ?
Question on how to construct wavelets to divide 2D frequency space in
polar coordinates??
I am interested in learning from our netters on the above question. I am
primarily interested in dividing a two dimensional frequency space in
polar coordinates: one octave bands in the radial direction and 4 or 5
regions in the angular direction. I would appreciate any reference to
articles/books and any kind of suggestions. I am relatively inexperienced
in wavelet theory.
Thanks for your attention.
--------------------------- Topic #5 -----------------------------------
From: J.C. Baltzer AG, Science Publishers
Subject: Contents Advances in Computational Mathematics
Advances in Computational Mathematics
Editors-in-Chief:
John C. Mason, Applied & Computational Mathematics Group, Royal Military
College of Science Shrivenham, Swindon, SN6 8LA, England
E-mail: mason@rmcs.cran.ac.uk
and
Charles A. Micchelli, Mathematical Sciences Department, IBM Research
Center, P.O. Box 218, Yorktown Heights, NY 10598, USA
E-mail: cam@yktvmz.bitnet
Contents Volume 1, issues 3 & 4
W. Dahmen, S. Prossdorf and R. Schneider:
Wavelet approximation methods for pseudodifferential equations II: Matrix
compression and fast solution, pp. 259 - 335
K.A. Cliffe, T.J. Garratt and A. Spence:
Eigenvalues of the discretized Navier Stokes equation with application to
the detection of Hopf bifurcations, pp. 337 - 356
J. Williams and Z. Kalogiratou:
Least squares and Chebyshev fitting for parameter estimation in ODEs, pp.
357 - 366
C.T.H. Baker and C.A.H. Paul:
Parallel continuous Runge Kutta methods and vanishing lag delay
differential equations, pp. 367 - 394
Please request a FREE SPECIMEN COPY from publish@baltzer.nl!
Advances in Computational Mathematics is an interdisciplinary journal of
high quality, driven by the computational revolution and emphasising
innovation, application and practicality. This journal is of interest to a
wide audience of mathematicians, scientists and engineers concerned with
the development of mathematical principles and practical issues in
computational mathematics.
Publication areas of Advances in Computational Mathematics include
computational aspects of algebraic, differential and integral equations,
statistics, optimization, approximation, spline functions and wavelet
analysis. Submissions are especially encouraged in modern computing aspects
such as parallel processing and symbolic computation and application areas
such as neural networks and geometric modelling.
All contributions should involve novel research. Expository papers are also
welcomed provided they are informative, well written and shed new light on
existing knowledge. The journal will consider the publication of lengthy
articles of quality and importance. From time to time special issues
devoted to topics of particular interest to the reader will be published
with the guidance of a guest editor. Ideas for special issues can be
communicated to the Editors-in-Chief.
Software of accepted papers is tested and made available to the readers on
Netlib. Short communications, a problems section and letters to the
Editors-in-Chief are also featured in the journal at regular intervals.
Advances in Computational Mathematics is being published quarterly.
Authors are cordially invited to submit their manuscripts in triplicate to
John C. Mason, Applied & Computational Mathematics Group, Royal Military
College of Science, Shrivenham, Swindon SN6 8LA, UK, E-mail:
mason@rmcs.cran.ac.uk
All manuscripts will be refereed. The decision for publication will be
communicated by John C. Mason. After acceptance of their paper, authors are
invited to send a diskette with the TEX (or LATEX or AMS-TEX) source of
their paper together with a hard copy including the letter of acceptance to
John C. Mason. For papers concerning software an ASCII diskette is needed.
Personal subscriptions; subscriptions in developing countries and how to
subscribe
A personal subscription to Advances in Computational Mathematics is
available at Sfr. 130.00/US$ 97.00 per volume including postage. The
personal subscription is meant for private use only and may not be made
available to institutes and libraries. Subscriptions must be prepaid
privately and ordered directly from J.C. Baltzer AG, Science Publishers,
Wettsteinplatz 10, CH-4058 Basel, Switzerland.
For institutions in developing countries, a subscription is available at
the special price of Sfr. 130.00/US$ 97.00 per volume including postage.
Subscriptions must be prepaid and ordered directly from J.C. Baltzer AG,
Science Publishers, Wettsteinplatz 10, CH-4058 Basel, Switzerland.
In the United States please send your order to: J.C. Baltzer AG, Science
Publishers, P.O. Box 8577, Red Bank, NJ 07701-8577.
>From all other countries please send your order to: J.C. Baltzer AG,
Science Publishers, Wettsteinplatz 10, CH-4058 Basel, Switzerland.
J.C. Baltzer AG, Science Publishers, Wettsteinplatz 10, CH-4058 Basel,
Switzerland, fax: +41 - 61 - 692 42 62, e-mail: publish@baltzer.nl
J.C. Baltzer AG, Science Publishers
Asterweg 1A, 1031 HL Amsterdam, The Netherlands
tel. +31-20-637 0061 fax. +31-20-632 3651
e-mail: publish@baltzer.nl
--------------------------- Topic #6 -----------------------------------
From: J.R.Klauder and R.F.Streater.
Subject: Preprint available
The following new preprint is available by E-mail from udah110@bay.cc.kcl.ac.uk
Wavelets and the Poincare Half-plane, by J.R.Klauder and R.F.Streater.
Abstract:We transform a square-integrable signal into an analytic function
in the upper half-plane, on which $SL(2,{\bf R})$ acts. We show that this
analytic function is determined by its scalar products with the discrete
family of functions obtained by acting with $SL(2,{\bf Z})$ on a certain
vector, provided that the spin of the representation is less that 3.
R.F.Streater.
--------------------------- Topic #7 -----------------------------------
From: Silvia Bertoluzza, IAN-CNR Pavia (Italy)
Subject: Preprints available
Preprint can be requested for the following papers:
"Some Remarks on Wavelet Interpolation"
by S. Bertoluzzza, G. Naldi
Abstract: In this paper we present some results regarding wavelet
interpolation. After discussing the characterization of interpolating
scaling functions we give two examples of construction of an interpolation
operator in the framework of a multiresolution analysis, the first obtained
by constructing an interpolating scaling function in a given multiresolution
analysis, and the second based on the autocorrelation function of a
compactly supported Daubechies wavelet. For both examples we give an
estimate on the order of the interpolation error.
--
"A wavelet Collocation Method for the Numerical Solution of PDE's"
Abstract:
We present a wavelet collocation method for the numerical solution
of partial differential equations. Such a method is based on the use of the
autocorrelation functions of I. Daubechies's compactly supported wavelets.
We study from the theoretical point of view
the application of such a method to the solution of an elliptic constant
coefficients partial differential equation on the line, proving stability and
an error estimate. Due to the particular
form of the trial functions we chose, we remark that we get the same
linear system which arises in the application of the wavelet Galerkin method
using
Daubechies wavelets. However, due to the higher regularity and to the better
approximation properties, the collocation method has higher order.
In the last section we will present results of such a method tested
on two simple elliptic boundary value problems on the interval.
---
Point of contact for preprint:
Silvia Bertoluzza,
IAN-CNR,
v. Abbiategrasso 209
27100 Pavia (Italy)
E-mail: Sil26@IPVIAN.bitnet
--------------------------- Topic #8 -----------------------------------
From: Jaideva C. Goswami, Dept. of Electrical Engineering, Texas A&M Univ.
Subject: Reply: Question Coeff. for the Chui wavelets, WD 2.14 # 9.
Note: The equation numbers are from the book, "An Introduction to Wavelets",
by C. K. Chui.
For Chui-Wang wavelets, the reconstruction sequences ({p_k},{q_k}) are
finite but the decomposition sequences ({a_k},{b_k}) are infinite with
exponential decay. Symbols of the decomposition sequences are related
to those of reconstruction sequences through (5.4.12). More explicit
relation is given by (6.5.1). Euler-Frobenius Laurent series that appears
in (6.5.1) is easy to compute for any order of spline (see 6.1.13). Then
the decomposition sequence can be obtained by comparing the corresponding
coefficients of powes of "z" on the both sides of (6.5.1). For this
purpose, use of symbolic computation package such as, MACSYMA, MAPLE, is
advisable.
Another simpler way of computing ({a_k},{b_k}) is given in Prof. Chui's
forthcoming book, "Wavelets: For Time-Frequency Analysis".
Jaideva C. Goswami
Dept. of Electrical Engineering
Texas A&M University
College Station, TX 77840 goswami@ee.tamu.edu
--------------------------- Topic #9 -----------------------------------
From: Jack K. Cohen <jkc@dix.mines.colorado.edu>
Subject: Mathematica wavelet program available.
I have put Mathematica packages and notebooks for construction of
the Meyer, Battle-Lemarie and Daubechies wavelets and
related functions in our anonomous ftp:
hilbert.mines.colorado.edu or 138.67.12.63
directory pub/wavelets.
All files are compressed, use `binary mode' in ftp.
The *.m.Z files are the packages.
The *.ma.Z files are NeXT-specific notebooks
Using nb2tex from mathsource, I converted the notebooks to Tex:
The *.300dpi.ps.Z are plain Tex, 300 dots per inch
The *.400dpi.ps.Z are plain Tex, 400 dots per inch
The implementations are "vanilla", derived from the
material in Ten Lectures. I.e., nothing new here,
the purpose is to save other Mathematica users from
having to recreate the functions for the basic wavelets.
Authors: Jack K. Cohen, Tong Chen, Meng Xu
Colorado School of Mines in Golden
jkc@dix.mines.colorado.edu
tchen@dix.mines.colorado.edu
mxu@dix.mines.colorado.edu
--------------------------- Topic #10 -----------------------------------
From: David Newland, Cambridge University Engineering Department
Subject: New Wavelet Toolbox in Matlab
NEW WAVELET TOOLBOX
As previously announced, the book Random Vibrations, Spectral and Wavelet
Analysis (John Wiley, New York, ISBN 0-470-22153-4 in the USA and Longman,
ISBN 0-582-21584-6 elsewhere) has an accompanying wavelet toolbox in
MATLAB*. This toolbox is now available separately from the book with an
accompanying descriptive manual. The expanded toolbox currently has 18
M-files for dilation and harmonic wavelet transforms and the presentation
of their results in signal analysis. There is also a short demonstration
program.
Harmonic wavelets have a simple analytical structure, a fast algorithm, are
orthogonal, and have many applications in signal analysis. Musical
wavelets are developments of harmonic wavelets which allow greater
frequency discrimination.
The programs compute the one-dimensional dilation wavelet transform and its
inverse,display the results of the transform, map the results as contour
and mesh diagrams, and compute two-dimensional dilation wavelet transforms
and their inverse. There are also programs to compute the harmonic wavelet
transform of a one-dimensional sequence, and its inverse and to compute the
harmonic wavelet map of a real sequence. This uses an algorithm based on
the FFT and, for most problems, is quicker than the dilation wavelet
transform. In addition there are programs to compute the musical wavelet
transform of a real signal and its inverse and to display the results of
this calculation in the form of a musical wavelet map. This has a
presentation similar to the musical stave and produces a diagram similar to
a sonogram.
Instructions on how to obtain the toolbox can be obtained by e-mail request
to den@eng.cam.ac.uk.
D E Newland
*MATLAB is a registered trademark of The MathWorks Inc.
Professor David Newland
Cambridge University Engineering Department
Trumpington St
Cambridge, CB2 1PZ, UK
--------------------------- Topic #11 -----------------------------------
From: dai@wuche2.wustl.edu (Xue-Dong Dai)
Subject: Workshop: Wavelets in Chemical Engineering
WASHINGTON UNIVERSITY in St. Louis, WORKSHOP
Sunday, November 7, 1993
1:00 - 5:45 PM Lopata Hall, Rm 101
Wavelets in Chemical Engineering
1:00 - 1:45 PM - Introduction and history of wavelet transforms
Srinivas Palavajjhala, Washington University
1:45 - 2:15 PM - Multiscale resolution, trend analysis
Amol Joshi, Aspen Technology
2:15 - 3:15 PM - Phase Plane Analysis, pattern recognition with demo.
Xue-dong Dai, Washington University
3:15 - 3:45 PM - Applications in process control
Srinivas Palavajjhala
3:45 - 4:15 PM - Data compression
Bhavik Bakshi, Ohio State
4:15 - 4:45 PM - Partial differential equations
Mike Nikolaou, Texas A&M
4:45 - 5:15 PM - Algorithms for wavelet transforms
Eric Goirand, Washington University
5:15 - 5:45 PM - "Wavelet's, etc. - what are they good for?"
Dr. M. V. Wickerhauser, Washington University
5:45 PM - Wrap-up
Contact: R. L. Motard, motard@cape1.wustl.edu or 314-935-6072
for hard copy and a map. FAX 314-935-7211.
-------------------- End of Wavelet Digest -----------------------------