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Wavelet Digest, Vol. 4, Nr. 2.



Wavelet Digest       Saturday, February 18, 1995             Volume 4 : Issue 2


Today's Editor: Wim Sweldens
                sweldens@math.scarolina.edu


Today's Topics:

      1. Book:     Wavelets and subband coding
      2. Preprint: Spherical wavelets
      3. Preprint: Wavelet transformations as diversity enhancers
      4. Preprint: Wavelet Coefficients of Functions of Lipschitz Classes
      5. Preprint: Partitioning eddy motion using Lorentz wavelet filtering
      6. Preprint: Monte Carlo Variance of Scrambled Equidistrib. Quadrature
      7. Preprint: SPIE reprints available from Jim Scholl
      8. Preprint: Biorthogonal Smooth Local Trigonometric Bases
      9. Preprint: The lifting scheme: A custom-design wavelet construction 
     10. Software: Wavelet-Galerkin Connection Coefficients Software
     11. Software: "The Elliptic Sinc Function"
     12. Software: MegaWave2 Announcement
     13. Software: Wavelet Toolbox in Khoros 2.0.1 
     14. Meeting:  Spline Functions and the theory of Wavelets
     15. Meeting:  UCLA short course Fuzzy Logic, Chaos, and Neural Networks
     16. Meeting:  Poster Papers for SPIE Orlando Wavelet
     17. Meeting:  Wavelets at the AMS Meeting in Orlando
     18. Meeting:  Wavelets at the AMS Meeting in Chicago
     19. Course:   Wavelets: Principles, Applications and Implementations
     20. Course:   Physical wavelets, with applications to remote sensing
     21. Position: Fellowships in the National University of Singapore
     22. Question: Wavelet analysis and geological images
     23. Question: Wavelet & Music
     24. Question: Looking for wavelet teaching material
     25. Question: Wavelets and Monte Carlo
     26. Question: Looking for  M-band wavelet software
     27. Question: Wavelets for rometely sensed images
     28. Question: Wavelets and convolution

Submissions:
  E-mail to wavelet@math.scarolina.edu with "submit" as subject.

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Preprints, references, and back issues can be obtained from our
information servers:
  Ftp:    ftp.math.scarolina.edu (/pub/wavelet)
  Gopher: gopher.math.scarolina.edu
  WWW:    <A HREF="http://www.math.scarolina.edu/~wavelet/">Here</A>


Current number of subscribers: 4289

Calendar of events:

*Jan-Apr  : Spline Functions and the theory of Wavelets, Montreal  WD 4.2  #14
*Mar 17-18: Wavelets at the AMS Meeting, Orlando                   WD 4.2  #17
*Mar 24-25: Wavelets at the AMS Meeting, Chicago                   WD 4.2  #18
 Apr 17-21: SPIE: Wavelet applications for dual use, Orlando       WD 3.14 #5
*May 17-20: Course: Wavelets: Principles, Applic. and Implement.   WD 4.2  #17
*May 22-24: Course: Fuzzy Logic, Chaos, and Neural Networks, UCLA  WD 4.2  #15
 May 30-Jun 3: Meeting of the Acoustical Society of America, DC    WD 4.1  #7
 Jun 26-30: ANU Wavelets Workshop, Canberra, Australia             WD 3.6  #6
 Jul  3-7 : SIAM ICIAM 95, Hamburg, Germany                        WD 3.19 #15
 Jul 13-14: SPIE: Mathematical Imaging: San Diego                  WD 4.1  #6
 Jul 24-28: Wavelets in Electromagnetics PIERS, Seattle            WD 3.18 #11
 Sep 17-21: ASME Wavelets in Vibrations and Acoustics, Boston      WD 3.17 #11

--------------------------- Topic #1 -----------------------------------
From: jelena@research.att.com "Jelena Kovacevic" 
Subject: Book: Wavelets and subband coding

                 WAVELETS AND SUBBAND CODING

	Martin Vetterli		       Jelena Kovacevic 
	UC Berkeley		       AT&T Bell Labs
	Berkeley, CA 94720	       Murray Hill, NJ 07974
	martin@eecs.berkeley.edu       jelena@research.att.com

1995, 483 pp, ISBN: 0-13-097080-8 
PRENTICE HALL, Englewood Cliffs, NJ 07632 

Over the past few years, wavelets and their discrete-time cousins,
filter banks, or, subband coding have been used in a variety of signal
processing applications. From work in harmonic analysis and
mathematical physics, and applications such as speech, image
compression and computer vision, different disciplines have built up
methods and tools now cast in the common framework of wavelets.   

Offering a unified view of this exciting field, Wavelets and Subband
Coding develops the theory in both continuous and discrete time, and
presents important applications. 

Chapter 1 gives an overview of the topics covered and introduces the
concept of multiresolution that is central in both theory and
applications. 

Chapter 2 is a review of fundamentals that makes the book
self-contained, and it includes discussions of vector spaces, Fourier
theory, signal processing and time-frequency analysis. 

Chapter 3 develops discrete-time linear expansions based on filter
banks or subband coding. The two-channel case is studied in
detail. The multichannel case as well as transmultiplexers are
developed and design examples are given. 

Chapter 4 develops wavelets, both with direct approaches and based on
filter banks, and describes wavelet series and their computation, as
well as the construction of modified local Fourier transforms. 

Chapter 5 discusses continuous wavelet and local Fourier transforms
that are used in signal analysis, as well as discretized versions
leading to frames.  

Chapter 6 addresses efficient algorithms for filter banks and wavelet
computations. 

Chapter 7 concludes coverage by describing signal compression where
filter banks and wavelets play important roles, including speech,
audio, image and video compression. Source coding using transforms,
quantization, and entropy coding are studied in detail, and the
usefulness of multiresolution coding in current applications is
discussed. 

In addition, each chapter includes numerous illustrative examples and
several appendices cover additional material. The book includes about
a hundred homework problems, and contains 130 illustrations and photographs.

TABLE OF CONTENTS

1   Wavelets, Filter Banks and Multiresolution Signal Processing
1.1 Series Expansions of Signals
1.2 The Multiresolution Concept
1.3 Overview of the Book 

2   Fundamentals of Signal Decompositions
2.1 Notations
2.2 Hilbert Spaces
2.3 Linear Algebra
2.4 Fourier Theory and Sampling
2.5 Signal Processing
2.6 Time-Frequency Representations
2.A Bounded Linear Operators on Hilbert Spaces
2.B Parametrization of Unitary Matrices
2.C Convergence and Regularity of Functions

3   Discrete-Time Bases and Filter Banks
3.1 Series Expansions of Discrete-Time Signals
3.2 Two-Channel Filter Banks
3.3 Tree-Structured Filter Banks
3.4 Multichannel Filter Banks
3.5 Pyramids and Overcomplete Expansions
3.6 Multidimensional Filter Banks
3.7 Transmultiplexers and Adaptive Filtering in Subbands
3.A Lossless Systems
3.B Sampling in Multiple Dimensions and Multirate Operations

4   Series Expansions using Wavelets and Modulated Bases
4.1 Definition of the Problem
4.2 Multiresolution Concept and Analysis
4.3 Construction of Wavelets Using Fourier Techniques
4.4 Wavelets Derived from Iterated Filter Banks and Regularity
4.5 Wavelet Series and Its Properties
4.6 Generalizations in One Dimension
4.7 Multidimensional Wavelets
4.8 Local Cosine Bases
4.A Proof of Theorem 4.5

5   Continuous Wavelet and Short-Time Fourier Transforms and Frames
5.1 Continuous Wavelet Transform
5.2 Continuous Short-Time Fourier Transform
5.3 Frames of Wavelet and Short-Time Fourier Transforms

6   Algorithms and Complexity
6.1 Classic Results
6.2 Complexity of Discrete Bases Computation
6.3 Complexity of Wavelet Series Computation
6.4 Complexity of Overcomplete Expansions
6.5 Special Topics

7   Signal Compression and Subband Coding
7.1 Compression Systems Based on Linear Transforms
7.2 Speech and Audio Compression
7.3 Image Compression
7.4 Video Compression
7.5 Joint Source-Channel Coding
7.A Statistical Signal Processing

--------------------------- Topic #2 -----------------------------------
From: Peter Schroeder (ps@math.scarolina.edu)
Subject: Preprint: Spherical wavelets

Title: Spherical wavelets: Efficiently representing functions on the sphere
Authors: Peter Schroeder and Wim Sweldens

Abstract:
Wavelets have proven to be powerful bases for use in numerical analysis and
signal processing.  Their power lies in the fact that they only require a
small number of coefficients to represent general functions and large data
sets accurately.  This allows compression and efficient computations.
Traditional constructions have been limited to simple domains such as
intervals and rectangles.  In this paper we present a wavelet
construction for scalar functions defined on surfaces and more
particularly the sphere.  Treating these bases in the fully biorthogonal
case we show how bases with custom properties can be constructed with the
lifting scheme. The bases are extremely easy to implement and allow fully
adaptive subdivisions. We give examples of functions defined on the sphere,
such as topographic data, bi-directional reflection distribution functions,
and illumination, and show how they can be efficiently represented with
spherical wavelets.

Industrial Mathematics Initiative, University of South Carolina,
Research Report 1995:01, available through anonymous ftp at 
ftp://ftp.math.scarolina.edu/pub/imi_95/imi95_1.ps or imi95_1.ps.gz
Color tif images available in imi_95/imi95_1.pix/*.tif.

--------------------------- Topic #3 -----------------------------------
From: Brani Vidakovic <brani@isds.Duke.EDU>
Subject: Preprint: Wavelet transformations as  diversity enhancers

Discussion Paper on Thresholding

A draft form of the manuscript:           

WAVELET TRANSFORMATIONS AS  DIVERSITY ENHANCERS

by Prem Goel and  Brani Vidakovic

is available at ftp anonymous:
 ftp isds.duke.edu: pub/brani/papers/lorentz.ps
or in compressed form as
                --//--              /lorentz.ps.Z

Short abstract:
Discrete wavelet transformations have became indispensable
analytical tools  in data compression and data denoising.
In this paper we give some
empirical accounts of  wavelet transformations and
propose novel thresholding and wavelet selection methods.
This is achieved via connections with {\it measures of inequality,}
that have been used in economics for a long time.
We compare our methods with standard
thresholding and wavelet selection procedures.

Comments, suggestions, and critiques welcome.

Brani Vidakovic,
ISDS Duke University, Old Chem 223A
Durham, NC 27708-0251 (919-684-8025).

--------------------------- Topic #4 -----------------------------------
From: Jyri Lippus <lippus@ioc.ee>
Subject: Preprint: Wavelet Coefficients of Functions of Lipschitz Classes

J. Lippus,

Wavelet Coefficients of Functions of Generalized Lipschitz Classes,	
Research report Math78/94, IOC.

Abstract:

In this paper we study the coefficients of
wavelet and multiresolution-type expansions of functions with
a given majorant of the modulus of continuity. 
We prove that
the coefficient criteria of ordinary Lipschitz classes hold for a slightly
larger class of majorants, namely those, satisfying the so-called
Bari-Stechkin condition. 

It is available on ftp://keeks.ioc.ee/pub/ioc/rep/math/math78.ps

Jyri Lippus
Institute of Cybernetics	Tel. 52 77 17
Akadeemia tee 21		Fax. 52 79 01
EE-0026 Tallinn, Estonia	e-mail  lippus@ioc.ee

--------------------------- Topic #5 -----------------------------------
From: Brani Vidakovic <brani@isds.Duke.EDU>
Subject: Preprint: Partitioning eddy motion using Lorentz wavelet filtering

Preprint available:

The partitioning of attached and detached eddy motion in the
atmospheric surface layer using Lorentz wavelet filtering

By Gabriel Katul and Brani Vidakovic

via anonymous ftp: isds.duke.edu
  /pub/brani/papers/
as
 -rw-r--r--  1 119      33        1996900 Feb  9 10:40 turbulwave.ps
or 
 -rw-r--r--  1 119      33         574818 Feb  9 10:41 turbulwave.ps.Z


Abstract:

       Townsend's (1976) attached eddy hypothesis states that the
turbulent structure in the constant stress layer can be decomposed
into attached and detached eddy motion.  This paper
proposes and tests methodology for
separating the attached and detached eddy motion from time series
measurements of velocity and temperature.
The proposed methodology is based on the time-frequency
localization and filtering capabilities of the orthonormal wavelet
transforms.  Using a relative entropy statistical measure, the
optimal wavelet basis is identified first.  The turbulence time
series measurements are then transformed into the wavelet domain
where the contribution of specific events in the time-frequency
domain are identified.  The filtering scheme utilizes a recently
constructed Lorentz thresholding methodology that successfully
eliminated all wavelet coefficients associated with the detached
eddy motion.  While this filtering scheme lacks the compression
efficiency of the classical Donoho and Johnstone's universal
thresholding model, it conserves the higher-order statistics and
important turbulence interactions related to the Reynolds stresses.
Following the filtering scheme, the attached eddy motion time
series is re-constructed by an inverse wavelet transform of the
non-zero wavelet coefficients.  The proposed partitioning
methodology for attached and detached eddy motion is tested using
$56 Hz$ triaxial sonic anemometer velocity and temperature
measurements above a uniform dry lake bed in Owens valley,
California,  for a wide range of atmospheric stability conditions.
 Validation that the wavelet filtered time series represented the
attached eddy motion is also discussed in the context of
conservation of turbulence energy and surface fluxes.

--------------------------- Topic #6 -----------------------------------
From: Art Owen <art@Playfair.Stanford.EDU>
Subject: Preprint: Monte Carlo Variance of Scrambled Equidistrib. Quadrature

Preprint:   Monte Carlo Variance of Scrambled Equidistribution Quadrature
Author:     Art B. Owen

Correspondence:    Dept of Statistics
                   Sequoia Hall
                   Stanford CA 94305

                   art@playfair.stanford.edu

Abstract:

  A method of numerical integration over the high dimensional
unit cube is studied.  The method combines equidistribution methods
and Monte Carlo, attaining the accuracy of the former, while
allowing error estimation through replication.

  The relevance to wavelets is as follows: the integrand is 
first written in a multivariate base b Haar resolution.  The
coarsest terms are integrated exactly.  Higher order terms 
make a contribution to the sampling variance of the estimated
integral.

  Along a judiciously chosen sequence for the number of evaluations
n, the variance of the estimate is o(1/n), as compared to the
usual O(1/n).
  

Availability:

  By anonymous ftp or WWW from playfair.stanford.edu.  Look
under technical reports, then under author = Owen.

--------------------------- Topic #7 -----------------------------------
From: jfs@Atrax.risc.rockwell.com (Jim Scholl)
Subject: Preprint: SPIE reprints available from Jim Scholl

Hello wavepeople,

I have two (2) reprints available from a couple of SPIE conferences.
If anybodywants a copy of one or both of these then e-mail me your
SURFACE mail address; these are not in electronic form at all.

Paper 1: reprint from "Wavelet Applications in Signal and Image Processing II,"
	 SPIE volume 2303, 27-29 July 1994, San Diego, California.

Title: Audio signal compression with circular wavelet packets

Authors: J. F. Scholl and D. Rogovin

Abstract: We have successfully compressed audio signals using wavelet packets 
          based on a recently developed fast wavelet transform (FWT) scheme 
          using circular convolution with an adaptive hybrid filter / basis
          system.  This algorithm gives perfect reconstruction of the data;
	  edge effects are removed entirely.  As a result, the quality of audio
	  compression is much improved.  To illustrate this, we present results
          from our comparison study where we compressed a test signal using 
   	  these 'circular wavelet packets' and wavelet packets based on 
	  the standard FWT [i.e. with symmetric data padding] 
   
Paper 2: reprint from "Visual Communications and Image Processing '94," SPIE
	 volume 2308, 25-29 September 1994, Chicago, Illinois.

Title: Image enhancement of the galaxy VV371c using the 2D fast wavelet 
       transform.

Author: James F. Scholl

Abstract: The fast wavelet transform (FWT) for images developed by Mallat is a
    	  useful and powerful tool for image processing, with its main 
  	  applications being compression, feature extraction, and image 
 	  enhancement.  In particular, since this algorithm segments an image
	  with respect to both spatial frequency and orientation, image 
	  enhancement becomes more precise and efficient.  This idea is 
	  demonstrated by the removal of background noise and flaws from two 
	  digitized images of the faint galaxy VV371c.  This object was first
	  studied in the early 1980's using older and less sophisticated 
	  technologies and image processing techniques.  We present results of
	  the wavelet based image analysis of VV371c which yield new conclusions
	  as to the galaxy's structure and morphological classification.

Jim Scholl
Rockwell Science Center
1049 Camino Dos Rios
Thousand Oaks, CA 91360

Ph: (805) 373-4277
e-mail: jfs@risc.rockwell.com

--------------------------- Topic #8 -----------------------------------
From: Wim Sweldens (sweldens@math.scarolina.edu)
Subject: Preprint: Biorthogonal Smooth Local Trigonometric Bases

Title: Biorthogonal Smooth Local Trigonometric Bases
Author: Bjorn Jawerth and Wim Sweldens

Abstract:

In this paper we discuss smooth local trigonometric bases.
We present two generalizations of the orthogonal basis of
Malvar and Coifman-Meyer: biorthogonal and equal parity bases.
These allow natural representations of constant and, sometimes,
linear components.  We study and compare their approximation
properties and applicability in data compression. This is
illustrated with numerical examples. 

Industrial Mathematics Initiative, University of South Carolina,
Research Report 1994:05, available through anonymous ftp at 
ftp://ftp.math.scarolina.edu/pub/imi_94/imi94_5.ps or imi95_5.ps.gz.

Status: to appear in Journal of Fourier Analysis and Applications.

--------------------------- Topic #9 -----------------------------------
From: Wim Sweldens (sweldens@math.scarolina.edu)
Subject: Preprint: The lifting scheme: A custom-design wavelet construction 

Title: The Lifting Scheme: A Custom-Design Construction
       of Biorthogonal Wavelets
Author: Wim Sweldens

Abstract:

We present the lifting scheme, a new idea of constructing compactly
supported wavelets with compactly supported duals. The lifting scheme
provides a simple relationship between all multiresolution analyses with
the same scaling function. It isolates the degrees of freedom remaining
after fixing the biorthogonality relations. Then one has full control
over these degrees of freedom to custom-design the wavelet for a particular
application. It also leads to a faster implementation of the fast wavelet
transform. We illustrate the use of the lifting scheme in the construction of
wavelets with interpolating scaling functions.

Industrial Mathematics Initiative, University of South Carolina,
Research Report 1994:07, available through anonymous ftp at 
ftp://ftp.math.scarolina.edu/pub/imi_94/imi94_7.ps or imi95_7.ps.gz.

--------------------------- Topic #10 -----------------------------------
From: Juan Restrepo <restrepo@mcs.anl.gov>
Subject: Software: Wavelet-Galerkin Connection Coefficients Software


Wavelet-Galerkin Connection Coefficients Software

I am making available the software for the calculation of 
the matrix entries corresponding to inner produts of n-tuple 
wavelets and their derivatives. This makes up 
for a belated promise -no, I am not a politician 8-) - to 
provide users connection coefficient tables. 

FTP:
anonymous ftp to
info.mcs.anl.gov
file is
ntuples.tar.gz

WWW:
http://www.mcs.anl.gov/people/restrepo/index.html


Juan Mario Restrepo
Mathematics and Computer Science Division         
Bldg. 221 Argonne National Laboratory 9700 S Cass Ave Argonne IL 60439
e-mail:               restrepo@mcs.anl.gov
www-home page:        http://www.mcs.anl.gov/people/restrepo/index.html

--------------------------- Topic #11 -----------------------------------
From: "Soltis James Dr." <soltis@server.uwindsor.ca>
Subject: Software: "The Elliptic Sinc Function"
   
      Of promininant importance in communications theory is the
   sinc function ,or the Sa(sampling function), or simply
   (sin(x)/x).These are,of course all the same. Let us
   replace the trig sine function in sinc with the Jacobian
   elliptic sine function and study the new sinc. In particular
   we study the absolute value of the DFT or FFT of the 
   new function (sn(x,m)/x) . Here m is the modulus squared
   since MATLAB will now be used. In particular the result
   is quite interesting . Whereas the standard (sine(x)/x))
   provides a typical [ square-wave cum Gibbs response] the 
   switch from sine(m=0) to arbitrary m<1  shows a multi-level
   hierarchy of flat-levels(cum diminished Gibbs) with the
   number of levels increasing with m(!!).A family is born. 
   For example,with m=0.4 there are a few levels and at
   m=0.999999999999 there are about 15 for the 1-sided
   spectrum.Typically 4096 points are used and only
   the simple rectangular windowing is done.
            The programs to show this effect can be 
   obtained by email from soltis@uwindsor.ca
   and use Windows-Matlab 4.0  .It should be trivial to   
   translate to other platforms, although high precision
   is needed for m near 1.   I used the digits command
   from the symbolic toolbox.I can think of applications
   in approximation theory and perhaps time-domain-reflectrometry
   but I find the scaling nature of the repeated steps
   similar to fractals.Since the function sn appears  
   in the solution of some non-linear DE's ,e.g. the
   simple pendulum, this may not be so surprising.
   The actual sinc plots are roughly similar to the
   standard case but have very slow roll-off near m=1.
   Any comments or questions are welcome.
           James Soltis, Univ. of Windsor,Windsor,Canada.   

--------------------------- Topic #12 -----------------------------------
From: mw@ceremade.dauphine.fr
Subject: Software: MegaWave2 Announcement

			MegaWave2 Announcement

I am pleased to announce you that the new version of the image processing 
software "MegaWave", called "MegaWave2", is now available by "anonymous
ftp" on the Internet at the following addresses: 

	mu.ceremade.dauphine.fr	(192.134.120.6)
		(directory pub/software)
			&
	ftp.univ-paris5.fr		(193.48.200.13)
		(directory pub/Unix/Image/MegaWave)

This package from the CEREMADE (Paris-IX Dauphine university, France) includes
up-to-date algorithms about (the source files are given):

	- Wavelets (at this time, orthonormal and bi-orthonormal wavelets only);
	- Affine Morphological Scale Space;
	- Snakes;
	- Segmentation.

Registration is requested but with no fee for educational and public research 
purposes (you must fill and send a registration form included in the package).

Sincerely,

 The MegaWave administrator. 
 E-mail : MegaWave@ceremade.dauphine.fr
 CEREMADE, Universite Paris-IX       
 75775 Paris cedex 16, France.       
 Fax : (33-1) 44.05.45.99            

--------------------------- Topic #13 -----------------------------------
From: jonio@tucumcari.khoros.unm.edu (Jonio R. H. Cavalcanti)
Subject: Software: Wavelet Toolbox in Khoros 2.0.1 

			ANNOUNCEMENT

This is to officially announce the release of the

	Wavelet Toolbox in Khoros 2.0.1 

It is available via ftp from "ftp.khoros.unm.edu" (198.59.155.28)
in the directory /pub/khoros/khoros2.0/contrib/toolboxes/wavelet.  Other
distribution sites will be posted at a later date.

This toolbox is comprised of basic rotines for performing general
wavelet transformations on data objects (1D to 5D).  In addition, there
are routines to manipulate the transformed objects.  The Wavelet Toolbox 
can be installed as an additional toolbox with Khoros 2.0.1.

This toolbox was the result of a joint venture between the Ibero-American 
Science and Technology Education Consortium (ISTEC), Khoral Research, Inc. 
(KRI), University of Campinas (UNICAMP - BRAZIL), University of Vigo 
(UVIGO - SPAIN), and the University of New Mexico (UNM - USA).  In addition,
a brief description of the toolbox was presented at the COST\#229 
Workshop on Adaptive Systems, Intelligent Approaches, Massively Parallel
Computing and Emergent Techniques in Signal Processing and Communications,
in Bayona (Vigo), Oct. 19-21, 1994.

         Jonio Roberto de Hollanda Cavalcanti
         University of New Mexico New Mexico - USA
	 Phone: (505) 837 - 6500 Ext. 303 email - jonio@khoros.unm.edu

--------------------------- Topic #14 -----------------------------------
From: Jean-Marc Lina <lina@lps.umontreal.ca>
Subject: Meeting: Spline Functions and the theory of Wavelets
   

     The "Centre de Recherche Mathematique" (CRM) Theme Year 1995-1996
                     APPLIED and NUMERICAL ANALYSIS
                   
             "Spline Functions and the theory of Wavelets"
                   Montreal, January to April 1996
                  
                        ( first announcement )

  The Centre de Recherche Mathematiques is hosting a year-long  program
  in applied and numerical analysis in 1995-1996.  From january 1996 to
  april 1996, courses  and seminars will be  devoted to the splines and
  wavelets. It will bring together different experts of the theoretical
  and applied aspects of the field. This period will include  a variety
  of activities (courses, special days, informal seminars, etc.) and in
  particular a  workshop which will  be open to the whole community. We
  are also considering organizing a forum bringing together an eclectic
  group of  researchers in medicine,  engineering and industry  who are
  interested in problems where wavelets are applicable.A specific theme
  is assigned to each week as follows:

  - Jan 22 - Jan 26: Geometric Modelling with Splines
  - Jan 29 - Feb  2: Splines in approximation and for PDE
  - Feb 12 - Feb 16: Splines and wavelets
  - Feb 19 - Feb 23: Wavelets and approximation
  - Feb 26 - Mar  1: Multiresolution analysis and subdivision operators 
  - Mar  4 - Mar  8: Wavelets and differential equations
  - Mar 11 - Mar 15: Wavelets for signal processing and image analysis
  - Mar 18 - Mar 22: Wavelets and fractals
  - Mar 25 - Mar 29: Wavelets in physics
  - Apr  9 - Apr 12: Splines and wavelets in statistics


Organizers: M. Bilodeau (U. of Montreal, Montreal)
            G. Deslauriers (Polytechnique, Montreal)
            S. Dubuc (CRM and U. of Montreal, Montreal)
            V. Hussin (CRM and Univ. of Montreal, Montreal)
            J.M. Lina (ANSL and U. of Montreal, Montreal)
            B. MacGibbon (UQUAM, Montreal)

The list of invited lecturers includes: 
  A. Antoniadis, A. Arneodo, B. Barsky, J.J. Benedetto, C. Chui, A. Cohen, 
  W. Dahmen, I. Daubechies, R.A. DeVore, N. Dyn, J. Geronimo, T. Goodmann,
  A. Grossmann,  H.P. Hardin,  N. Heckmann,  P. Holmes,  M. Holschneider, 
  S. Jaffard, K. Jetter,  J. Klauder, S. Mallat,  A. Le Mehaute, Y. Meyer, 
  C. Miccheli,  R. Murenzi,  T. Paul,  D. Picard,  S.D. Riemenschneider, 
  P. Sablonniere, G. Strang, P. Tchamitchian,  J. Villasenor,  G. Walter
  

Those wishing to participate in the above activities are invited to write
to 
                       Louis Pelletier, 
                  CRM, University of Montreal, 
                  C.P. 6128, Suc. Centre-Ville
                  Montreal, (Qu.) H3C 3J7 
                  CANADA
                  
   or e-mail to     pelletl@crm.umontreal.ca

--------------------------- Topic #15 -----------------------------------
From: "Goodin, Bill" <BGoodin@UNEX.UCLA.EDU>
Subject: Meeting: UCLA short course on Fuzzy Logic, Chaos, and Neural Networks

On May 22-24, 1995, UCLA Extension will present the short course,
"Fuzzy Logic, Chaos, and Neural Networks: Principles and
Applications", on the UCLA campus in Los Angeles.

The instructor is Harold Szu, PhD, Research Physicist,
Washington, DC.

This course presents the principles and applications of
several different but related disciplines--neural
networks, fuzzy logic, chaos--in the context of pattern
recognition, control of engineering tolerance
imprecision, and the prediction of fluctuating time
series.  Since research into these areas has contributed
to the understanding of human intelligence, researchers
have dramatically enhanced their understanding of fuzzy
neural systems and in fact may have discovered the
"Rosetta stone" to decipher and unify these intelligence
functions.  For example, complex neurodynamic patterns
may be understood and modelled by Artificial Neural
Networks (ANN) governed by fixed-point attractor dynamics
in terms of a Hebbian learning matrix among bifurcated
neurons.  Each node generates a low dimensional
bifurcation cascade towards the chaos but together they
form collective ambiguous outputs; e.g., a fuzzy set
called the Fuzzy Membership Function (FMF).  This
feature becomes particularly powerful for real world
applications in signal processing, pattern recognition
and/or prediction/control.  The course delineates the
difference between the classical sigmoidal squash function
of the typical neuron threshold logic and the new N-shaped
sigmoidal function having a "piecewise negative logic" that can
generate a Feigenbaum cascade of bifurcation outputs of which
the overall envelope is postulated to be the triangle FMF.  The
course also discusses applications of chaos and collective
chaos for spatiotemporal information processing that has been
embedded through an ANN bifurcation cascade of those collective
chaotic outputs generated from piecewise negative logic neurons.
These chaotic outputs learn the FMF triangle-shape with a
different degree of fuzziness as defined by the scaling function of
the multiresolution analysis (MRA) used often in wavelet transforms.
Another advantage of this methodology is information processing
in a synthetic nonlinear dynamical environment.  For example,
nonlinear ocean waves can be efficiently analyzed by nonlinear
soliton dynamics, rather than traditional Fourier series.
Implementation techniques in chaos ANN chips are given.

The course covers essential ANN learning theory and the
elementary mathematics of chaos such as the bifurcation cascade
route to chaos and the rudimentary Fuzzy Logic (FL) for those
interdisciplinary participants with only basic knowledge of the
subject areas.  Various applications in chaos, fuzzy logic, and
neural net learning are illustrated in terms of spatiotemporal
information processing, such as:

 --Signal/image de-noise
 --Control device/machine chaos
 --Communication coding
 --Chaotic heart and biomedical applications.

For additional information and a complete course description,
please contact Marcus Hennessy at:
(310) 825-1047
(310) 206-2815  fax
mhenness@unex.ucla.edu

--------------------------- Topic #16 -----------------------------------
From: hszu@relay.nswc.navy.mil (Harold Szu)
Subject: Meeting: Poster Papers for SPIE Orlando Wavelet

Call for Post Deadline Poster Papers for SPIE Orlando Wavelet
Applications 1995 April 17-21 at Marriott's Orlando World Center. The
deadline of final manuscripts is Feb 10 1995 received at SPIE Office.

Since the last call for papers, we have received over hundred
submissions to Orlando Wavelet Applications II, which is the
continuation of the last year Wavelet Applications Conference at
Orlando.  Due to the delay over the Seasons Greetings in the last
month, SPIE Conf. manager Don Grandstrom (206-647-1445 Fax), and
Proceedings Editor Sheila Sandiford (206 676 3290 X451) have agreed to
postpone the deadline to 10th Feb 1995 received at SPIE WA Office COB.

This year, in addition to FBI, ARPA, ONR, NAWC, NSWC sponsor
participations, we have NIST/ATP Program managers to describe NIST
programs including Data Compressions.  Also,the $15 Mil AFIS program of
FBI has been distributed this Spring.  One believes that R/D efforts of
telecommunications using WT will become viable alternatives for
National Information Infrastructure.

We would like to call your attention to participate in the post
deadline poster paper submission, which will be published in the
Proceeding Vol 2491, divided according to 14 technical Sessions without
any indication as regard to the format of presentations. You will have
a chance to briefly describe your posters in a two viewgraphs & two
minutes oral introduction on Wednesday evening reception.  Again, this
year, there will be Best Poster Paper Awards based on your votes.

There will be no formal mats for submitting this paper. You should
consult any other SPIE Camera Ready 8x11' single column format without
page limit, and mail a copy to me & to SPIE indicating postdeadline
poster paper for Proc. Vol. 2491.


Harold Szu, Conf. co-chair
(301) 394-3097 (O)
(301) 394-3923 (Fax)
e-mail: hszu@ulysses.nswc.navy.mil

Note from the editor: for the full conference announcement check WD 3.14 #5

--------------------------- Topic #17 -----------------------------------
From: Donna Salter <DLS@MATH.AMS.ORG>
Subject: Meeting: Wavelets at the Orlando AMS Meeting

Friday, March 17, 1995, 9:30 a.m.--10:50 a.m.  
Special Session on Sampling Theory, Wavelets and Signal Processing, I
Organizer: Ahmed I. Zayed, University of Central Florida 
     
 9:30-9:50: Colella, D.
  Wavelet-based processing of $EEG$ waveforms.-Preliminary report. 
  David Colella, The MITRE Corporation 
     
 10:00-10:20: Aldroubi, A.
  Oblique projections in unitary-invariant spaces, biorthogonal 
  multi-wavelets, and sampling.
  Akram Aldroubi, National Institute of Health 
     
 10:30-10:50: Heil, C.
  Perturbing frames, Banach frames, and atomic decompositions.
  Christopher Heil*, Georgia Institute of Technology, and  
  Ole Christensen, Technical University of Denmark, Denmark 
     
Friday, March 17, 1995, 2:30 p.m.--5:50 p.m.  
Special Session on Sampling Theory, Wavelets and Signal Processing, II
Organizer: Ahmed I. Zayed, University of Central Florida 
     
 2:30-2:50: Harrison, M. L.
  Localization and computational efficiency in frame irregular sampling.
  Preliminary report. 
  John J. Benedetto, 
  Melissa L. Harrison*, University of Maryland, College Park, and  
  William H. Heller, University of Texas-Pan American 
     
 3:00-3:20: Nashed, M. Z.
  Sampling expansions and moment discretization problems.
  M. Z. Nashed, University of Delaware 
     
 3:30-3:50: Walter, G. G.
  Multiwavelets orthogonal in a Sobolev sense.
  Gilbert G. Walter, University of Wisconsin, Milwaukee 
     
 4:00-4:20: Zayed, A. I.
  Sampling in a Hilbert space.
  Ahmed I. Zayed, University of Central Florida 
     
 4:30-4:50: Mugler, D. H.
  Computational aspects of an $SVD$-based method for linear prediction of a
  band-limited signal from past samples.
  Dale H. Mugler, University of Akron 
     
 5:00-5:20: Kon, M. A.
  Determining functions from zeroes of their wavelet transforms.
  Mark Andrew Kon, Boston University 
     
 5:30-5:50: Heller, W. H.
  A method for computing nonharmonic Fourier series.-Preliminary report. 
  William H. Heller, University of Texas-Pan American 
     
Saturday, March 18, 1995, 2:30 p.m.--5:50 p.m.  
Special Session on Sampling Theory, Wavelets and Signal Processing, III 
Organizer: Ahmed I. Zayed, University of Central Florida 
     
 2:30-2:50-253-Hudgins, L. H.
  A real-time denoising filter based on the wavelet maxima representation.
  Preliminary report. 
  Lonnie H. Hudgins, Northrop Electronics Systems Division, California 
      
 3:00-3:20-254-Jerri, A. J.
  The Gibbs phenomenon--An update and recent results.
  Abdul J. Jerri, Clarkson University 
     
 3:30-3:50-255-Faridani, A.
  Periodic sampling and computed tomography.
  Adel Faridani, Oregon State University 
     
 4:00-4:20-256-Walnut, D. F.
  New sampling results and applications.
  David F. Walnut, George Mason University 
     
 4:30-4:50-257-Casey, S. D.
  An algorithm for isolating periodicities from a sparse set of noisy measurements.
  Stephen D. Casey, American University 
     
 5:00-5:20-258-McCoy, P. A.
  Applications of signal processing methods to boundary-initial value problems.
  Preliminary report. 
  P. A. McCoy, United States Naval Academy and United States Naval 
  Research Laboratory 
     
 5:30-5:50-259-Raphael, L. A.
  Convergence rates of wavelet expansions.
  Mark Andrew Kon, Boston University, and  
  Louise A. Raphael*, Howard University 


Friday, March 17, 1995, 2:30 p.m.--4:50 p.m.  
Special Session on Wavelets for PDEs and Integral Equations, I
Organizer: Wim Sweldens, University of South Carolina
     
 2:30-2:50: Auscher, P.
  On adapted wavelet bases for some differential operators.
  Pascal Auscher, Brown University 
     
 3:00-3:20: Hardin, D.
  Multiwavelets and diagonalizing bilinear forms.
  Doug Hardin, Vanderbilt University

 3:30-3:50: Bray, W. O.
  Approximate identities and Calderon type reproducing formulas on the 
  circle group.-Preliminary report. 
  William O. Bray, University of Maine, Orono 

 4:00-4:20: Dahlke, S.
  A posteriori error estimates for wavelet Galerkin methods.
  Stephan Dahlke, University of South Carolina 
     
 4:30-4:50: Bihari, B. L.
  Multiresolution schemes for the numerical solution of conservation laws.
  Barna L. Bihari, Rockwell Science Center, Thousand Oaks, California 


Saturday, March 18, 1995, 8:30 a.m.--10:50 a.m.  
Special Session on Wavelets for PDEs and Integral Equations, II
Organizer: Wim Sweldens, University of South Carolina
     
 8:30-8:50: Weiss, J.
  Wavelets, turbulence and boundary value problems for partial 
  differential equations.
  John Weiss, Aware, Inc., Cambridge, Massachusetts 
      
 9:00-9:20: Williams, J. R.
  An element free boundary point method based on wavelet radial basis functions.
  Preliminary report. 
  John R. Williams* and  
  Kevin Amaratunga, Massachusetts Institute of Technology 
       
 9:30-9:50: Bond, D. M.
  Fast wavelet transforms for matrices arising from boundary element methods.
  Dave M. Bond*, 
  Stephen A. Vavasis, Cornell University, Ithaca, and  
  Palghat S. Ramesh, Xerox Corporation 
     
 10:00-10:20: Schroder, P.
  Wavelet algorithms for illumination computations.
  Peter Schroder, University of South Carolina, Columbia 
     
 10:30-10:50: Jiang, A.
  Fast wavelet methods for time dependent problems.
  Stanley Osher and  
  A. Jiang*, University of California, Los Angeles 

--------------------------- Topic #18 -----------------------------------
From: Donna Salter <DLS@MATH.AMS.ORG>
Subject: Meeting: Wavelets at the Chicago AMS Meeting

Friday, March 24, 1995, 9:00 a.m.--10:50 a.m.  
Special Session on Extensions and Applications of Harmonic Analysis: Spaces of
Homogeneous Type and Wavelet Analysis, I 
     
 9:00-9:20: Cohen, J.
  Wavelet analysis in recruitment of loudness compensation.
  Laura Drake, 
  J. C. Rutledge, Northwestern University, and  
  Jonathan Cohen*, DePaul University 
     
 9:30-9:50: Whitmal, N. A.
  Wavelet-based noise reduction for speech enhancement.
  N. A. Whitmal*, 
  J. C. Rutledge, Northwestern University, and  
  J. Cohen, DePaul University 
     
 10:00-10:20: Goldberg, M. J.
  Denoising a recording of Caruso using local trigonometric bases with 
  $1_p$ entropy as cost function.-Preliminary report.
  Jonathan Berger, 
  Ronald R. Coifman, Yale University, and  
  Maxim J. Goldberg*, York University 
     
 10:30-10:50: Saito, N.
  Simultaneous denoising and compression of signals/images using a library 
  of local orthonormal bases and the MDL criterion.
  Naoki Saito, Schlumberger-Doll Research, Ridgefield, Connecticut 
     

Friday, March 24, 1995, 3:00 p.m.--5:50 p.m.  
Special Session on Extensions and Applications of Harmonic Analysis: Spaces of
Homogeneous Type and Wavelet Analysis, II 
     
 3:00-3:20: Han, Y.
  Biframe on spaces of homogeneous type.-Preliminary report.\ 
  Y.S. Han, Auburn University, Auburn 
     
 3:30-3:50: Nahmod, A. R.
  Multiscale analysis and spectral geometry of operators.-Preliminary report.\ 
  Andrea R. Nahmod, University of Texas, Austin 
     
 4:00-4:20: Hofmann, S.
  An ``off-diagonal'' T1 theorem and applications.
  Steve Hofmann, University of Missouri, Columbia 
     
 4:30-4:50: Gatto, A. E.
  Fractional differentiation and integration on spaces of homogeneous type.
  A. Eduardo Gatto*, 
  Stephen V\'agi, DePaul University, and  
  Carlos Segovia, Universidad de Buenos Aires, Argentina 
     
 5:00-5:20: V\'agi, S.
  On the smoothness of functions which arise as potentials on spaces
  of homogeneous type.-Preliminary report.\ 
  A. Eduardo Gatto and  
  Stephen V\'agi*, DePaul University 
     
 5:30-5:50: Thiele, C. M.
  A new proof for the Carleson Hunt theorem for Walsh Fourier series.
  Christoph Martin Thiele, Yale University 
     
Saturday, March 25, 1995, 8:00 a.m.--10:50 a.m.  
Special Session on Extensions and Applications of Harmonic Analysis: Spaces of
Homogeneous Type and Wavelet Analysis, III 
     
 8:00-8:20: Wang, K.
  The full T1 theorem for certain Triebel-Lizorkin spaces.
  Kunchuan Wang, Michigan State University 
     
 8:30-8:50: Torres, R. H.
  Some remarks on the approximation of functions in Besov spaces using 
  band-limited wavelets.-Preliminary report.\ 
  Rodolfo H. Torres, University of Michigan, Ann Arbor 
     
 9:00-9:20: Wickerhauser, M. V.
  Multiplication of short wavelet series using connection coefficients.
  Mladen Victor Wickerhauser*, Washington University, and  
  Valerie Perrier, \'Ecole Normale Superieure, France 
     
 9:30-9:50: Weiss, G. L.
  Methods for constructing new wavelets.
  Xiang Fang, E. Hernandez, Xihua Wang and  
  Guido L. Weiss*, Washington University 
     
 10:00-10:20: Frazier, M. W.
  Function space norm equivalences for interpolating wavelets.
  Preliminary report.\ 
  David Donoho, Stanford University, and  
  Michael W. Frazier*, Michigan State University 
     
 10:30-10:50: Taibleson, M.
  Applications of harmonic analysis to the theory of harmonic Bloch functions 
  on a homogeneous tree.-Preliminary report.\ 
  Mitchell Taibleson, Washington University 

Saturday, March 25, 1995, 3:00 p.m.--5:20 p.m.  
Special Session on Extensions and Applications of Harmonic Analysis: Spaces of Homogeneous Type and Wavelet Analysis, IV 
     
 3:00-3:20: Sweldens, W. F.
  Construction and application of second generation wavelets.
  Wim F. Sweldens, University of South Carolina, Columbia 
     
 3:30-3:50: Weiss, J.
  Wavelets, turbulence and boundary value problems for partial differential 
  equations.
  John Weiss, Aware, Incorporated, Cambridge, Massachusetts 
     
 4:00-4:20: Restrepo, J. M.
  Wavelet-Galerkin discretization of hyperbolic equations.
  Juan Mario Restrepo* and  
  Gary K. Leaf, Argonne National Laboratory 
     
 4:30-4:50: Cai, L.
  Band limited interpolating multiwavelets.
  Gilbert G. Walter and  
  Luchuan Cai*, University of Wisconsin, Milwaukee 
     
  5:00-5:20: Fan, D.
  A restriction theorem and its application.
  Dashan Fan, University of Wisconsin, Milwaukee 

--------------------------- Topic #19 -----------------------------------
From: DRGROSSM@teexnet.tamu.edu
Subject: Course: Wavelets: Principles, Applications and Implementations

Announcement of Short Course

Wavelets: Principles, Applications and Implementations, May 17-20, 1995,
Texas A&M University in College Station, Texas.

This short course features Charles K. Chui, mathematician, A.K. Chan,
electrical engineer, and S. Liu, 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
continuous wavelet transform, and real-time preprocessing of a
continuous signal using cardinal splines. You will learn how to construct
wavelets, and how to use wavelet packets for frequency domain
fine-tuing in the hands-on laboratory sessions.

Lively interaction and question and answer sessions with the instructors
allow participants to reinforce theoretical concepts while learning from
each other and sharing experiences.

For registration information or to request a brochure, please contact
Marilynn Grossman. Email: drgrossm@teexnet.tamu.edu
Phone:800/447-9470 or 409/862-4615; Fax: 409/845-5726

--------------------------- Topic #20 -----------------------------------
From: lee@ee.eng.ohio-state.edu (Robert Lee)
Subject: Course: Physical wavelets, with applications to remote sensing

                             SHORT COURSE ANNOUNCEMENT:

PHYSICAL WAVELETS, WITH APPLICATIONS TO REMOTE SENSING

TIME:     Monday, March 20, 1995, 8:30AM-5PM
PLACE:  11th Annual Review of Progress in Applied Computational  
              Electromagnetics,  Naval Postgraduate School, 
              Monterey, CA, March 20-25, 1995
LECTURER:  Dr. Gerald Kaiser, Department of Mathematical Sciences,
                  University of Massachusetts Lowell

There will be four 90-minute lectures:

1.  Continuous time-frequency and time-scale methods.
2.  Multiresolution analysis and Daubechies wavelets.
3.  Introduction to electromagnetic and acoustic wavelets.
4.  Applications to remote sensing and communication:
     A variational approach to radar and sonar.

For more information, please contact:
Dr. Robert Lee, Ohio State University, EE Department
2015 Neil Ave., Columbus, OH 43210-1272
phone (614) 292-1433,  fax (614) 292-7596
email:    lee@ee.eng.ohio-state.edu

--------------------------- Topic #21 -----------------------------------
From: Hwee Huat Tan <mattanhh@nus.sg>
Subject: Position: Fellowships in the National University of Singapore

      Fellowships on Wavelets in the National University of Singapore

Two positions of post-doctoral fellowships are available in 
the area of WAVELETS, tenable in the 

                 Department of Mathematics, 
              National University of Singapore, SINGAPORE. 

One fellowship in on wavelet theory and the other on applications.
The post-doctoral position is meant for fresh Ph.D's.  Each fellowsihp
is for a  period of two years and offers a monthly salary of about S\$3,500
per month. 
More details and application forms may be obtained from 

                    Dr. Shen Zuowei 
                Department of Mathematics
             National University of Singapore 
               10 Kent Ridge Crescent, Singapore 0511
             e-mail address:  matzuows@leonis.nus.sg

--------------------------- Topic #22 -----------------------------------
From: roques@srvdec.obs-mip.fr (sylvie roques)
Subject: Question: Wavelet analysis and geological images

My name is Philippe Gaillot, and I am a student in Geophysics.
I would like to test wavelet analysis on geological images (2D) but
I have no software do do this.
My aim is to exhibit the size distributions of minerals and
shape form anisotropy.
Could someone indicate me where finding an adaptive software.
My E-mail is michel@lucid.ups-tlse.fr
Thank you very much in advance,

Philippe Gaillot

--------------------------- Topic #23 -----------------------------------
From: Regis Rossi Alves Faria <regis@ravel.lsi.usp.br>
Subject: Question: Wavelet & Music

I would like to contact people researching wavelets for computer
music applications.  I am working with wavelets in the
signal processing approach, with special interest in music analysis
and synthesis.

Looking forward this,

Regis Rossi A. Faria
LSI - Lab. Integrated Systems University of Sao Paulo Brazil
(regis@lsi.usp.br)

--------------------------- Topic #24 -----------------------------------
From: jsolka%tilki3@relay.nswc.navy.mil (Jeff Solka)
Subject: Question: Looking for wavelet teaching material

I am scheduled to teach a lower graduate/upper undergraduate
course in wavelets this summer. I would like to teach it from the
standpoint of wavelets for classification of both 1-d and 2-d
signals/images. I would appreciate any inputs regarding
texts, software, or other teaching materials.
Please write to me at

jsolka@tilki3.nswc.navy.mil

Thanks for any and all help.

Jeff Solka
  Code B10
  Systems Research and Technology Department
  Advanced Computation Technology Group
  Naval Surface Warfare Center Dahlgren, VA 22448-5000
  (703)-663-1982 phone (703)-663-1952 FAX
  jsolka@relay.nswc.navy.mil

--------------------------- Topic #25 -----------------------------------
From: "John J. Sasso Jr." <sassoj@rpi.edu>
Subject: Question: Wavelets and Monte Carlo

    Has anyone done any work with wavelets in conjunction with the
Monte Carlo method?  Have there been any papers on the subject (or
closely related to it)?

			John

--------------------------- Topic #26 -----------------------------------
From: jfs@Atrax.risc.rockwell.com (Jim Scholl)
Subject: Question: Looking for  M-band wavelet software

Hello,

Do any of you out there know where I can obtain C or Fortran codes for simple
M-band wavelet transforms on signals or images?  Thanks in advance!

Jim Scholl

Mathematical Physics Department
Rockwell Science Center 1049 Camino Dos Rios Thousand Oaks, CA 91360
ph (805) 373-4277 email: jfs@risc.rockwell.com

--------------------------- Topic #27 -----------------------------------
From: Thierry Ranchin <tr@armelle.cma.fr>
Subject: Question: Wavelets for rometely sensed images

Dear All,

I am searching informations on the use of wavelet transforms and
multiresolution analysis in the field of remotely sensed images.
I am searching news, bibliographies, postcript versions of articles,
web pages, ...  on the related subject
If you have informations please feel free of contacting me

I will post the responses If I receive some.

Thanks

Thierry Ranchin                      

 Groupe Teledetection & Modelisation  
 Centre d'Energetique                  e-mail : ranchin@cenerg.cma.fr
 Ecole des Mines de Paris             
 BP 207                                    tel : (33) 93 95 74 53
 F-06904 Sophia Antipolis Cedex            fax : (33) 93 95 75 35

--------------------------- Topic #28 -----------------------------------
From: Elharti Abdelmoula /ADVISOR Shoaff <rcs63223@tuck.cs.fit.edu>
Subject: Wavelets and convolution

 Dear waveleters,

In the FFT case, we know that for two vectors, taking the product of their FFT,
is the same as taking the inverse FFT of their convolution.
However, my question is: is it possible to apply this same type of anology
in the case of wavelets. If yes, how ? Or, is there a solution for that ?
                                                   Thank you.
                             Moula.

-------------------- End of Wavelet Digest -----------------------------