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Conference rusure::math

Title:Mathematics at DEC
Moderator:RUSURE::EDP
Created:Mon Feb 03 1986
Last Modified:Fri Jun 06 1997
Last Successful Update:Fri Jun 06 1997
Number of topics:2083
Total number of notes:14613

955.0. "wavelet & time-frequency display" by PRSUD1::CHALEAT () Fri Oct 21 1988 10:13

    hi,
    I am looking for references on WAVELETS or any kind of time-frequency
    representations.
    Does anyone has heard about?
    marcel
     
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955.1such things existCTCADM::ROTHLick Bush in '88Fri Oct 21 1988 22:014
    It sounds like you want a joint time/frequency representation such
    as the Wigner distribution, but you'll have to be more specific.

    - Jim
955.2more on waveletsPRSUD1::CHALEATTue Oct 25 1988 08:3427
    
    thanks,you are right.
    I have seen time-frequency representation of signals showing much
    more features than the usual one obtained from Fourier transform.
    The underlying maths exceed my level ,and look  rather esoteric
    at least for me !
    At the last european signal processing conference it was a paper
    on "time scale representations obtained with wavelets".
    I can send you a copy if you are interested and if you provide
    me your mail address.
    Basically the transform for a signal s(t) is:
    
    	S(t,a) = //  s(b) f((t-b)/a) db
    
    from which is derived
    
    	S(t,a) = //  g^'(au) s^(u) exp(jtu) du 
    
    where g is the analyzing wavelet which is a bell shaped pulse
    
    I used following symbols:
    up arrow ^   for fourier transform
    apostroph '  for complex conjugation
    pair of back slashes // for the integral symbol.
                        
              marcel