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From: cdc@uafhcx.uucp (C. D. Covington)
Newsgroups: comp.dsp
Subject: Discussion on Combining Samples
Summary: Prolate Spheroidal Wave Functions
Message-ID: <4714@uafhp.uark.edu>
Date: 2 Jun 90 17:00:44 GMT
Sender: netnews@uafhp.uark.edu
Organization: College of Engineering, University of Arkansas, Fayetteville
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   What signal results if you take an arbitrary function like a rectangular
pulse, run it through an ideal lowpass filter, and then time limit the result
back to say -T to +T seconds?  What do you get when you repeat this process
over and over?  Prolate spheroidal wave functions!  The resulting waveform
depends only in form on the time bandwidth product BT, where B is the band-
width and T is the time limit.  

   The primary references to work in this area follow.

D. Slepian and H. O. Pollack, "Prolate spheroidal wave functions, Fourier
   analysis and uncertainty - I," BSTJ, vol. 40, no. 1, pp. 43-63, Jan. 1961.

H. J. Landau and H. O. Pollack, "Prolate spheroidal wave functions, Fourier
   analysis and uncertainty - II," BSTJ, vol. 40, no. 1, pp. 65-84, Jan. 1961.

BSTJ = Bell System Technical Journal

   These functions have the interesting property that a maximum of spectral
energy is concentrated in a given (lowpass) bandwidth for a function of fixed
energy and non-zero only in some interval (-T,T).

   I came across these references when researching my paper, "Finite Support
Basis Functions With Minimum Shifted Remodeling Error".  Unfortunately the
paper was turned down by the ASSP so I can't give a reference.


C. David Covington (WA5TGF)  cdc@uafhcx.uark.edu     (501) 575-6583
Asst Prof, Elec Eng          Univ of Arkansas        Fayetteville, AR 72701