cdc@uafhcx.uucp (C. D. Covington) (06/03/90)
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