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From: Randy Yates <yates@ieee.org>
Newsgroups: comp.soft-sys.matlab,comp.dsp
Subject: Re: DFT the same as sampled Foureir transform?
Date: Thu, 24 May 2007 13:10:32 -0400
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"Mike" <meatheadIV@gmail.com> writes:
> [...]
> I agree my question is not well-posed. Here is a reformulation:
>
> Given a continuous time signal x(t), infinitely long. Sample it to obtain 
> discrete time sequence x0, x1, x2, ..., xn, ..., infinitely long, with 
> uniform samples spaced at T apart.
>
> Now I do two things:
>
> (1) Truncate the above sequence to make it finite, x0, x1, ..., xn, and take 
> the DFT of the truncated sequence. Call the DFT F1(v). (Capitalized letters 
> denote spectrum domain)
>
> (2) Without truncation, taking the DTFT of the infinitely long sequence x0, 
> x1, ..., xn, .... Call the DTFT F2(v). And then take one period of F2(v), 
> since it is periodic, and then sample F2(v) in the frequency domain to 
> discretize it. Call the result F3(v), which is the discretized version of 
> the one period of F2(v).
>
> ---------------------
>
> Both (1) and (2) yield vectors of length n in the spectrum domain, 
> representing the discretized version of the spectrum.
>
> My question is: under what conditions do these two vectors of discretized 
> spectrum equate?

When x(t) is periodic with period n*T.
-- 
%  Randy Yates                  % "Maybe one day I'll feel her cold embrace,
%% Fuquay-Varina, NC            %                    and kiss her interface, 
%%% 919-577-9882                %            til then, I'll leave her alone."
%%%% <yates@ieee.org>           %        'Yours Truly, 2095', *Time*, ELO   
http://home.earthlink.net/~yatescr