Thread Subject: Doppler <-> Bessel

http://en.wikipedia.org/wiki/Rayleigh_fading

If you take a look at that, it says the FFT of a bessel
function is supposed to be a doppler spectrum

B=besselj(0,0:.1:100);
Bfft=abs(fft(B));
figure
subplot(2,1,1)
plot(B)
subplot(2,1,2)
plot(Bfft)

this code agrees with that nicely.

However, if I go the other way:

LengthDoppler = 1002;
fm=4;
StepSize = 2 * fm / (LengthDoppler - 1);
f = (fc - fm) : StepSize : (fc + fm);
DopplerSpectrum = 1 ./ (pi * fm * sqrt(1 - ((f-fc)/fm).^2));
DopplerSpectrum = DopplerSpectrum(2 : (end - 1));

where the last line is to throw away infinity points (one on
each end)

plot(DopplerSpectrum) looks nice as expected

however
plot(abs(ifft(DopplerSpectrum))) produces another doppler
spectrum, not a bessel function!!! Can anyone explain that /
give me a hint on how to fix it?

Thanks,

David