HILBERT TRANSFORM

[Fred Herzfeld <herzfeld@xxxxxxxxxxxx>]

Hello list,

Suppose I have a finite sampled set of data of length 2^n of a function
s(t) = cos(2*pi*f-phi) where f and phi are constant with time and s(t)
is sampled at time intervals so that s(t) falls exactly into the second 
FFT bin. If I perform the FFT, modify the output by 90 degrees and 
perform an inverse FFT, the output of the FFT will be exactly the 
Hilbert Transform of the original series s(t) namely HT[s(t)].

Now I repeat the same process except that I change the frequency (still 
constant) to 7*f/8 and call the time series S1(t). The output of the FFT 
will now contain many non zero bins. In theory I should still be able to 
modify the FFT output and do the inverse FFT to get the Hilbert 
Transform of S1(t).

(1)	Can I really compute HT[S1(t)] correctly ?
(2)	If I can, how should the output of the FFT of S1(t) be modified

Any thoughts on this will be very much appreciated.

Fred

--
Fred Herzfeld, MIT '54
78 Glynn Marsh Drive #59
Brunswick, Ga.31525
USA