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Wavelet Digest, Vol. 4, Nr. 7.



Wavelet Digest           Friday, June 23, 1995            Volume 4 : Issue 7


Today's Editor: Wim Sweldens
                Katholieke Universiteit Leuven, Belgium
                wim.sweldens@cs.kuleuven.ac.be


Today's Topics:

     1. Book:     An Introduction to Wavelets using MATLAB (in Spanish)
     2. Preprint: Wavelet analysis for brain-function imaging
     3. Program:  Time-Frequency/Scale Analysis for Navy Applications (ONR)
     4. Meeting:  Siggraph 95 Wavelet course 
     5. Meeting:  UK Symposium on Time-Frequency/Scale Methods
     6. Meeting:  Acoustical Society of America
     7. Contents: JAT Vol. 81, No. 3, June 95
     8. Question: HARC-C?
     9. Question: Wavelets to analyze transient signals
    10. Question: Window Fourier Transform

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Current number of subscribers: 4881


--------------------------- Topic #1 -----------------------------------
From: Carlos Enrique D'Attellis <ceda@clami.edu.ar>
Subject: Book: An Introduction to Wavelets using MATLAB (in Spanish)


       An Introduction to Wavelets using MATLAB (in Spanish)

Authors: C.E. D'Attellis, M.I. Cavallaro, M. Anaya and F. Villaverde


	This 97 pages beginner's guide contains an intuitive approach
for engineering students. It also presents complete MATLAB programs
covering the most important issues, from Fourier and Windowed Fourier
Transforms to polynomial splines in a multiresolution framework.

	Different examples are shown.


				C.E. D'Attellis
				University of Buenos Aires
				E-Mail: ceda@clami.edu.ar


					Carlos Enrique D'Atttellis
					ceda1@clami.edu.ar

--------------------------- Topic #2 -----------------------------------
From: Rene Carmona <rcarmona@chelsea.math.uci.edu>
Subject: Preprint: Wavelet analysis for brain-function imaging

Preprint on Brain Imaging available by anonymous ftp. The paper is 
to appear in the IEEE Transactions on Medical Imaging

Title: WAVELET ANALYSIS FOR BRAIN-FUNCTION IMAGING

Authors: Rene A. Carmona, Wen L. Hwang and  Ron D. Frostig

Abstract:

The purpose of the paper is to present a new algorithmic procedure for
the analysis of brain images. This procedure is specifically designed
to image the activity and the functional organization of the brain.
Our results are tested on data collected and previously analyzed with
the technique known as in vivo optical imaging of intrinsic signals.
Our procedure enhances the applicability of this technique and
facilitates the extension of the underlying ideas to other imaging
problems (e.g. functional MRI). The thrust of the paper is
twofold. First we give a systematic method to control the blood vessel
artifacts which typically reduce the dynamic range of the image.

We propose a mathematical model for the vibrations in time of the
veins and arteries and we design a new method for cleaning the images
of the vessels with the highest time variations. This procedure is
based on the analysis of the singularities of the images. The use of
wavelet transform is of crucial importance in characterizing the
singularities and in reconstructing appropriate versions of the
original images. The second important component of our work is the
analysis of the time evolution of the fine structure of the images. We
show that, once the images have been cleaned of the blood vessel
vibrations/variations, the principal component of the time evolutions
of the signals is due to the functional activity following the
stimuli. The part of the brain where this function takes place can be
localized and delineated with precision.

To get a copy (the postscript file compressed with gzip):

ftp chelsea.math.uci.edu
username: anonymous
password: your e-mail address
binary 
cd pub
cd outgoing
cd signalproc
get chf.ps.gz
quit

Let me know if you have any problem retrieveing the file.

                          rcarmona@uci.edu


--------------------------- Topic #3 -----------------------------------
From: Lake, Douglas <LAKED@onrhq.onr.navy.mil>
Subject: Program: Time-Frequency/Scale Analysis for Navy Applications (ONR)


    Time-Frequency / Time-Scale Analysis for Navy Applications


The Office of Naval Research is pleased to announce a new initiative in
the area of time-frequency and time-scale analysis. For stationary
signals, short time Fourier transforms (STFT) or spectrograms have been
used successfully by the Navy for many years for signal analysis. Time-
frequency distributions have been shown to be effective representations
for certain classes of nonstationary signals (e.g., chirp signals). Wavelet
analysis techniques perform well in isolating features of nonstationary
signals that occur at multiple scales and/or are compactly supported in
time. These current time-frequency and time-scale analysis approaches
have had mixed success with applications (i.e., real data) in the presence
of noise and/or with signals composed of diverse multiple components.

The objective of the initiative is to develop a unifying and
mathematically rigorous theory of time-frequency analysis and apply
new time-frequency techniques and methodologies to nonstationary,
multiple component, noisy signals that occur in high priority Navy
applications. Time-frequency analysis theory embodies both
distributional and  wavelet approaches and can be embedded and
understood in mathematical frameworks utilizing statistical, operator-
theoretic, and group theoretic methods (among others). Applications of
interest include radar imaging (e.g., ISAR), vibrational and motor
current analysis for mechanical diagnostics, and the classification of
underwater mines from acoustic backscatter. Optimal and
computationally efficient time-frequency processing (vice FFT) is
needed for radar imaging to  increase resolution for maneuvering (time-
varying Doppler) targets. Time-frequency energy representations
(preferably positive) are needed to isolate and characterize mechanical
faults that occur  in both time and frequency.  Time-frequency analysis
is needed to identify and extract nonstationary components (e.g.,
specular echo, resonant frequencies, etc.) from an acoustic response that
discriminate mines from clutter (e.g. rocks).

Interested parties are encouraged to submit short (5 pages) technical
white papers to ONR describing their research by September 30, 1995
for initial evaluation. Selected authors will be encouraged to submit
formal proposals by March 31, 1996. Successful proposals will be
funded starting October 1, 1996.  Submit technical material to and for
additional information please contact:

                       Dr. Douglas E. Lake
            Program Officer, Signal and Image Analysis
   Surveillance, Communications and Electronic Combat Division
                Office of Naval Research, Code 313
                   Arlington, VA 22217-5660 USA
                       703-696-6567 (Voice)
                        703-696-1331 (Fax)
                     laked@onrhq.onr.navy.mil

--------------------------- Topic #4 -----------------------------------
From: Alain Fournier <fournier@cs.ubc.ca>
Subject: Meeting: Siggraph 95 Wavelet course 

SIGGRAPH 95

     Wavelets and Their Applications in Computer Graphics

Date: Monday August 6 (Full day)

Course syllabus

In the past few years wavelets have been developed both as a new
analytic tool in mathematics and as a powerful set of practical
tools
for many applications from differential equations to image processing.
Wavelets and wavelets transforms are important to researchers
and practitioners in computer graphics because they are a natural
step from classic Fourier techniques in image processing, filtering
and reconstruction, but also because they hold promises in shape
and light modelling as well.
It is clear that wavelets and wavelet transforms can become as
important and ubiquitous in computer graphics as spline-based technique
are now.

This course is intented to give the necessary mathematical background
on wavelets, and explore the main applications, both current and
potential, to computer graphics. The emphasis is put on the connection between
wavelets and the tools and concepts which should be familiar to
any skilled computer graphics person: Fourier techniques, pyramidal
schemes, spline representations. 

- Introduction

Scale and Frequency
Scale: Playing with the pyramid
Frequency: Fourier analysis
Limitations of global transforms
Windowed Fourier Transforms
Continuous Wavelet Transforms
>From Continuous to Discrete
Image Pyramids revisited
Haar Transform as a Case Study
Multi-dimensional Wavelets

- Mathematical Properties and Formulations of Wavelets

Dyadic and Discrete Wavelet Transforms
Multiresolution Analysis
Orthogonality and Bi-orthogonality
Approximation Properties
Constructing a Wavelet Basis
Daubechies and Spline (Battle-Lemarie) wavelets

- Image Processing Applications

Signal Compression
Multiscale Edge Detection and Reconstruction
Time vs Space vs Direction
Painting with wavelets

- Curve and Surface Modelling

Properties for Curve and Surface representation
Building the right wavelet
Multiresolution curve representation
Multiresolution Surface representation
Curve and Surface Design with Wavelets

- Wavelet Projections

Projection Methods
Operators on Wavelet Basis
Application to Radiosity Solutions

- Other Applications and Conclusions

Light Flux Representation with Wavelets
Solving Differential and Integral Equations
Fractals and Wavelets
Future Trends

- Discussion and Conclusions 

Course Lecturers

Michael Cohen is currently at Microsoft.  He was previously Assistant
Professor at the Department of Computer Science at Princeton
University. He is one of the originators of the radiosity approach for
global illumination. He has used in his own research wavelet
techniques for curve modelling and hierarchical space-time control.
email address: mfc@CS.Princeton.EDU

Tony DeRose is Associate Professor at the Department of Computer
Science at the University of Washington.  His main research interests
are computer aided design of curves and surfaces, and he has applied
wavelet techniques in particular to multiresolution representation of
surfaces.  email address: derose@cs.washington.edu

Michael Lounsbery did his PhD at the University of Washington under
the supervision of Tony DeRose, where he developed techniques for the
multiresolution analysis for surfaces of arbitrary topological type.
email address: louns@cs.washington.edu

Alain Fournier is a Professor in the Department of Computer Science at
the University of British Columbia.  His research interests include
modelling of natural phenomena, filtering and illumination models.
His interest in wavelets derived from their use to represent light
flux and to compute local illumination within a global illumination
algorithm he is currently developing.  email address:
fournier@cs.ubc.ca

Leena-Maija Reissell is a Research Associate in Computer Science at
UBC, on leave from XOX Corporation, Minneapolis, Minnesota.  Ms
Reissell is currently conducting research in curve and surface
approximation with wavelet bases.  email address: reissell@cs.ubc.ca

Peter Schro\*:der completed his doctoral studies in Computer Science
at Princeton University. His research activities have included dynamic
modelling for computer animation, massively parallel graphics
algorithms, global illumination algorithms, and most recently the
application of wavelets to hierarchical radiosity algorithms.  He has
currently a Post Doctoral position at the University of South Carolina
in Columbia.  email address: ps@math.scarolina.edu

Wim Sweldens is a Research Assistant of the Belgian National Science
Foundation at the Department of Computer Science of the Katholieke
Universiteit Leuven, and a Research Fellow at the Department of
Mathematics of the University of South Carolina.  His research
interests include the construction of second generation wavelets and
their applications in numerical analysis and image processing.  email
address: sweldens@math.scarolina.edu

Summary statement

This course is intented to give the necessary mathematical background
on wavelets, and explore the main applications, both current and
potential, to computer graphics. The emphasis is put on the connection
between wavelets and the tools and concepts which should be familiar
to any skilled computer graphics person: Fourier techniques, pyramidal
schemes, spline representations, solution of linear systems.

Course objectives

The immediate objective of the course is to provide enough background
on wavelets so that a researcher or skilled practitioner in computer
graphics can understand the nature and properties of wavelets, and
assess their suitability to solve specific problems in computer
graphics.  To achieve this, we will use the natural connections
between wavelets and many techniques familiar in computer graphics. We
will as well describe and analyse current applications. After the
course the attendees should be able to access the basic mathematical
literature on wavelets, understand and review critically the current
computer graphics literature using them, and have some intuition about
the pluses and minuses of wavelets and wavelet transform for a
particular application with which they are familiar.

Course prerequisites

General knowledge of computer graphics is necessary. A good background
in signal or image processing will help. You should be fine if you are
familiar with at least two of the following topics: Fourier
transforms, image pyramids, MIP maps, NIL maps, vector spaces, solving
systems of linear equations.

Intended audience

Researchers and advanced practitioners in computer graphics, who are
currently trying to solve problems in image representation and
compression, curve and surface representation, light representation
and propagation, shading and illumination models.


We will again include basic software with the course, the UBC Wavelets
library written by Bob Lewis, based on last year's issue, but enlarged
and improved.


--------------------------- Topic #5 -----------------------------------
From: "Stuart Lawson" <esrhy@eng.warwick.ac.uk>
Subject: Meeting: UK Symposium on Time-Frequency/Scale Methods

UK Symposium on Applications of Time-Frequency and Time-Scale Methods

TFTS'95
30th and 31st August 1995

University of Warwick, Coventry, UK

Sponsored by IEEE SP Chapter (UKRI Section) in collaboration with 
University of Warwick and IEE.

Draft Programme May 1995


Wednesday 30th August


09.00 Welcome Stuart Lawson (University of Warwick)

09.15 Keynote Lecture Leon Cohen (Hunter College,NY)

Session 1 Wavelets Chair: Franz Hlawatsch

10.15 Tutorial 1 Paul Bentley (University of Edinburgh)

10.45 Coffee Break

11.15 Tutorial 2 Roland Wilson (University of Warwick)

12.00 Dr Ph.Guillemain and Dr P.R.White (UK)
Wavelet Transforms for the Analysis of Dispersive Systems 

12.20 Dr J.Hall and J.Crowe (UK)
Ambulatory Electrocardiogram Compression using Wavelet Packets to 
Approximate the Karhunen-Loeve Transform 

12.40 Lunch

Session 2 Image Processing Chair: Roland Wilson

14.00 Gu,Y.H.,W.Hermsen & R.A.Carrasco UK 
Image Motion Compensation and Coding Based on Transform-Domain 
Multiresolution Features and Classified Vector Quantisation

14.20 Liang,K.H.,T.Tjahjadi & Y.H.Yang UK/Canada  
A Regularized Multiscale Edge Detection Scheme Using Cubic-B Spline

14.40 Strela,V., P.N.Heller, G.Strang, P.Topiwala & C.Heil USA 
Application of Multiwavelets to Signal and Image Processing  

15.00 Trintinalia,L.C., H.Ling and S.Qian USA 
Joint Time-Frequency ISAR Image Processing Using Adaptive Gaussian 
Basis 
Functions 

15.20 Tea Break/Poster Session

Session 3 Acoustics Chair: John Arnold

15.50 Hughes,D. & L.Cohen USA 
Instantaneous Duration and Bandwidth in Acoustics Scattering   

16.10 Kudumakis,P.E. & M.B.Sandler UK
Synthesis/Coding of Audio Signals Based on Inverse Wavelet Packet 
Algorithm 

16.30 Mariuz,S. Italy 
Analysis, Separation and Synthesis of Musical Signals Spectrum 

19.00 Symposium Dinner


Thursday 31st August

09.00 Keynote Lecture Franz Hlawatsch (Austria)

Session 4 Vibration and Optics Chair: Leon Cohen

10.00 Matz,G.,F.Hlawatsch & W.Kozek Austria 
Weyl Spectral Analysis of Non-Stationary Random Processes 

10.20 Oehlmann,H.,D.Brie,V.Begotto & M.Tomczak France 
A Method for Analysing Gearbox Failures Using Time-Frequency 
Distributions 

10.40 Arnold,J.M. UK 
Gabor Transforms in Diffraction Theory  

11.00 Coffee Break/Poster Session

Session 5 Forum Discussion Chair: Stuart Lawson(Prov.)

11.30-12.30 Panelists include L.Cohen, R.Wilson, F.Hlawatsch and 
D.Chen

12.30 Lunch

Session 6 Communications Chair: Stuart Lawson

14.00 Argo,P.E.,M.J.Freeman & T.J.Fitzgerald USA 
Transionospheric Chirp Event Classifier  

14.20 Freeman,M.J.,M.E.Dunham.S.Qian & D.Chen USA 
Trans-Ionospheric Signal Detection by Time-Scale Representation  

14.40 Chen,V.C. & S.Qian USA 
Application of Joint Time-Frequency Transform to Inverse Synthetic 
Aperture 
Radar 

15.00 Tea/Poster Session

Section 7 Audio Chair: Mark Sandler

15.30 X.Wei & M.J.Shaw UK 
High Quality Audio Nonuniform Subband Coding Using Frequency Warping 

16.00 Wilson,R.,T.Shuttleworth & H.R.R.Scott UK 
Representations for Audio Signal Analysis  

16.30 Closing Remarks  Stuart Lawson

Poster Sessions
Chair: Stuart Lawson

1. Hlawatsch,F. and H.Bolcskei Austria 
Time-Frequency Distributions Based on Conjugate Operators 

2. Konig,D.& J.F.Bohme Germany 
Application of Wigner-Ville Spectrum Analysis for Optimization of 
Sensor 
Positions  

3. Astrade,F. France 
Time-Frequency Image Processing: Mathematical Morphology  

4. Camilleri,K.,N.Fatemi-Ghomi,P.L.Palmer and M.Petrou UK 
Zak Transform and its Application to Image Processing  

5. Ademovic,E.,J.C.Pesquet,P.Attal & G.Charbonneau France 
Time-Frequency Classification of Infantile Laryngo-Tracheal Sounds  

6. Rodriguez,M.A. & L.Vergara Spain 
Microcracks Detection on Ceramic Materials Using Wigner-Ville 
Transform NDT

7. Huggett,C. & P.Bryanston-Cross UK 
An Analysis of Spatial and Temporal Optical Measurements made on a 
Musical 
Instrument Optics 

8. Andina,D.,J.Torres,J.Martinez-Cristobal & R. Gomez-Sanchez Spain 
Wavelet Pre-Processing and Neural Networks for Sonar Detection 

9. Chevret,P. & F.Magand France 
Time-Frequency Analysis of Stoneley Wave Energy Distribution for 
Spherical 
and Cylindrical Shells.

10. Navarro-Mesa,J.L. Spain 
Optimum Window Length in Speech Signals Time-Frequency Analysis  

11. Bolcskei,H.,H.G.Feichtinger & F.Hlawatsch Austria 
Diagonalising the Gabor Frame Operator Theory  

12. Zeng,H. France 
Signal Distortion During Overlap-Add Synthesis Caused by Spectral 
Modification 
and its Correction in Audio Restoration 
 
13. Chitti,Y. France 
Application of Image Processing in Neurobiology: Detection of Low 
Signals 
with High Spatial Resolution and a Non Uniform Variance Medicine

14. Prelcic,N.G. & D.D.Amoedo Spain 
A Multipulse-like Wavelet based Speech Coder 

For further information on the programme or registration contact the 
symposium chair
Dr Stuart Lawson
Department of Engineering
University of Warwick
Coventry
UK
tel:  01203-523780
fax: 01203-418922
e-mail: s.lawson@eng.warwick.ac.uk

--------------------------- Topic #6 -----------------------------------
From: "trappe" <trappe@arlut.utexas.edu>
Subject: Meeting: Acoustical Society of America

Part I:
------

Hi-

I am writing on behalf of the Signal Processing Committee for the
Acoustical Society of America to inform you about a Gallery of Signal
Processing in Acoustics that will take place at the St. Louis Meeting
of the ASA on November 27 - December 1, 1995.

A gallery of images and videos depicting signals or processes in
Acoustics is planned for the St. Louis meeting of the
ASA. Contributions are invited from all technical areas of Acoustics.
The gallery will be on display during the meeting and entries will be
judged by a panel of referees on the basis of originality, the ability
to convey and exchange information, and aesthetic appeal.  Entries may
be in the form of either a poster or a short video.  Publication and
future display of outstanding entries is being considered.

Poster entries will be displayed on vertical panels and hence should
be mounted by the contributor on poster board or cardboard panels
measuring no larger than 2.5 ft wide by 3 ft. high.  In addition to
the artwork, each panel should contain a brief text explaining the
display, as well as the names and affiliations of the contributors.

Video entries must be submitted in VHS or S-VHS format (PAL can not be
converted) with a total running time of no more than three
minutes. Entries should contain visual material but may emphasize
visual information, audio information, or both.  Tapes should begin
with a 20 second blank leader followed by the three minute entry.
Entries must contain the title, names and affiliations of the
contributors.  All entries will be copied onto a single tape prior to
the meeting and shown in a continuous, posted order on a monitor with
stereo speakers.

Further inquiries should be made to David Havelock at (613) 993-7661,
or email david.havelock@nrc.ca.

Part II:
-------

Hello-

I am writing to inform you, the readers of the Wavelet Digest, of the
call for papers for the 130th Meeting of the Acoustical Society of
America.

The 130th Meeting of the ASA will be held Monday through Friday, 27
November - 1 December 1995 at the Adam's Mark Hotel in St. Louis,
Missouri.  Some sessions will be held on Monday and a full program of
sessions will be held every morning and afternoon, Tuesday through
Friday.  Registration will begin Monday at 7:30.

The deadline for receipt of abstracts is Monday, 31 July 1995. ***
This deadline will be strictly enforced.  Beginning with this meeting,
authors have the option of submitting their abstracts electronically,
or by mail in the standard paper-copy method.

Technical Program: Contributed papers are welcome in all branches of
acoustics.  The technical program will consist of lecture sessions and
some poster sessions.  The following special sessions are planned for
invited and contributed papers (note: due to the general nature of the
ASA, I am only listing the ones loosely relevant to the readers of the
wavelet digest... sorry...):

1. Acoustic Interactions with Internal Waves in Waves in Shallow Water.
2. Mechanical System Noise
3. Recent Advances in Hearing and Technology
4. Acoustic Instrument Callibration
5. Flow Induced Noise
6. Higher Order Spectrum and Trans-Spectrum
7. Exchange of Research Ideas and Findings Between Music and Speech Perception
8. Modeling Vowel Perception
9. Statistical Methods in Complex Structures
10. Wiener-Hopf Methods in Structural Acoustics
11. Spatial, temporal, and frequency dispersion due to boundary
    scattering inshallow water propagation.

To find out information on how to send abstracts, contact Elaine
Moran, ASA Office Manager at (516) 576-2360 (phone), or (516) 349-7669
(FAX).

If you are sending an electronic version of an abstract, the files
needed may be obtained by ftp from ftp.aip.org.  Login "anonymous" and
use your email address as the password. Change directory to
/tex/macros/asaabs and get all the files in the directory. Or you can
send email to asahelp@aip.org requesting for the ASA Abstracts package
by email and you will be send the files.  The package includes
instructions, a completed example and an empty template.

The Hotel Information: The Adam's Mark Hotel, Fourth and Chestnut,
St. Louis, MO 63102 has a block of rooms reserved at reduced
rates. The hotel number is (314) 241-7400; the fax number is (314)
241-0889. Refer to the Acoustical Society meeting to obtain the
reduced rates of $103/single, and $115/double.

Any additional information can be obtained from Elaine Moran, ASA
Office Manager at (516) 576-2360 (phone), or (516) 349-7669 (FAX).


Wade Trappe
Applied Research Laboratories
University of Texas at Austin

--------------------------- Topic #7 -----------------------------------
From: Marilyn Radcliff <radcliff@math.ohio-state.edu>
Subject: Contents: JAT Vol. 81, No. 3, June 95

Table of Contents: J. Approx. Theory, Volume 81, Number 3, June 1995

Ding-Xuan Zhou
On smoothness characterized by Bernstein type operators
303--315
Johan Lithner and Adam P. W\'ojcik
A note on Berntein's theorems
316--322
Ding-Xuan Zhou
Construction of real-valued wavelets by symmetry
323--331
E. Kochneff
Expansions in Laguerre polynomials of negative order
332--346
Graeme J. Byrne, T. M. Mills, and Simon J. Smith
The Lebesque constant for higher order Hermite-Fej\'er interpolation on
     the Chebyshev nodes
347--367
Peter K\"ohler and Geno Nikolov
Error bounds for Gauss type quadrature formulae related to spaces of
     splines with equidistant knots
368--388
Gilbert Helmberg
A limit function for equidistant Fourier interpolation
389--396
Peter K\"ohler and Geno Nikolov
Error bounds for optimal definite quadrature formulae
397--405
Xie Ping Ding and E. Tarafdar
Some further generalizations of Ky Fan's best approximation theorem
406--420
Notes
Horst Alzer
On the zeroes of a polynomial
421--424
Fernando Mazzone and H\'ector Cuenya
A note on metric projections
425--428

--------------------------- Topic #8 -----------------------------------
From: Harald Skardal <harald@ftp.com>
Subject: Question: HARC-C??

I read in PC Magazine, 95/05/16, about this wavelet 
based video/image compression work at Houston
Advanced Research Center. Is there anything one
can read on the Web about it that gives more detail?

Thx,

    Harald.

  Harald Skardal,		<harald@ftp.com>
  FTP Software.
  N. Andover, MA, USA.

--------------------------- Topic #9 -----------------------------------
From: eterray@whoi.edu
Subject: Question: Wavelets to analyze transient signals

          I would appreciate knowing of any work using wavelets to
          analyze the direction of arrival of transient signals
          measured with a spatial array - some sort of analysis that
          makes use of the cross-sensor phase information.

          Thanks -   E. Terray, Dept. Applied Ocean Physics & Engr.,
                     Woods Hole Oceanographic Institution
                     eterray@whoi.edu


--------------------------- Topic #10 -----------------------------------
From: Haikel Hichri <hah134@cs.usask.ca>
Subject: Question: Window Fourier Transform

Hello everyone

	I am currently studying wavelets.  I have a few questions
that I couldn't answer from the books and papers I am reading.

the question is about Windowed Fourier Transform :

I am reading in a lot of places (for example a fairly good book titled
" a freindly guide to wavelets " by Gerald Kaiser) about the
Heisenberg inequality and I don't understand why is it a problem.
now, the regular fourier analysis as i understand so far, has a
problem with discontiniouties which makes the fourier expansion to
include high frequency harmonics to aproxmate the function to a
certain degree. and these high frequency harmonics extend over the
whole time period, right..  ok, now they say that the WFT solves this
problem by looking at the function through windows, using a function g
suported on interval I.  that way only the coeficients near the
discontineouty are affected. or in other words only high frequency
harmonics supported on the interval I are needed.

	then they go on and prove the "Heisenberg inequality" which says
in the book mentioned above that dt.df>c where c is a constant and df
and dt are defined by the standard deviation of g divided by its
energy and df is the standard deviation of Fourier transform(g)
devided by the same energy again.  now they say this a problem because
two pulses closer than dt can't be descriminated and also tow waves
with frequencies closer than df can't be descriminated. but why? how
on earth did they get this result?  everybody talks about it as if it
is intiutive well it is not for me!
 this makes me even more confused : 
why this resolution problem exists for WFT but for the FT?  I have no
problem with the mathematical proof as usual but I don't understand
the meaning of it, the intuition behind it.

I hope this is clear enough.

i hope I will get an answer from you guys 
thanks,

Hichri Haikel              (H)(306) 373-4842
Department of Computer Science
University of Saskachewan, Saskatoon CANADA.

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