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From: "Mike" <meatheadIV@gmail.com>
Newsgroups: comp.soft-sys.matlab,comp.dsp
Subject: Re: DFT the same as sampled Foureir transform?
Date: Thu, 24 May 2007 10:20:26 -0700
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"Randy Yates" <yates@ieee.org> wrote in message 
news:m37iqydu5z.fsf@ieee.org...
> "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

Thanks Randy! The original signal x(t) is not periodic. I guess my next 
question is:

How to handle such a situation and get an approximation error that is as 
small as possible?