The Wavelet Digest Homepage
Return to the homepage
Search the complete Wavelet Digest database
Help about the Wavelet Digest mailing list
About the Wavelet Digest
The Digest The Community
 Latest Issue  Back Issues  Events  Gallery
The Wavelet Digest
   -> Volume 4, Issue 7

Question: Window Fourier Transform
images/spacer.gifimages/spacer.gif Reply into Digest
Previous :: Next  
Author Message
Haikel Hichri (

PostPosted: Tue Dec 03, 2002 1:22 pm    
Subject: Question: Window Fourier Transform
Reply with quote

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

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

All times are GMT + 1 Hour
Page 1 of 1

Jump to: 

disclaimer -
Powered by phpBB

This page was created in 0.024197 seconds : 18 queries executed : GZIP compression disabled