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Reply-To: "Nasser Abbasi" <nma@12000.org>
From: "Nasser Abbasi" <nma@12000.org>
Newsgroups: comp.soft-sys.matlab,comp.dsp
References: <f33fqk$2f8$1@news.Stanford.EDU>
Subject: Re: DFT the same as sampled Foureir transform?
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Date: Thu, 24 May 2007 01:51:03 -0700
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"Mike" <meatheadIV@gmail.com> wrote in message 
news:f33fqk$2f8$1@news.Stanford.EDU...
> Hi all,
>
> I have the following question regarding the relation between DFT and 
> Foureir Transform.
>
> Suppose I have a sequence of discrete time signal x0, x1, x2, ... xn, ... 
> (possibly infinite length), uniformly spaced in time, with spacing T; 
> that's to say, x0 is the signal value at time 0, x1 is the signal value at 
> time 1*T, x2 is the signal value at time 2*T, ...
>
> and the DFT of this sequence is F1(v).
>
> Also, for this sequence of signal, I have an ordinary Foureir Transform 
> F2(v), I guess it's called DTFT.
>
> I plan to sample the F2(v) to obtain the discrete version of the F2(v) and 
> call it F3(v).
>
> My question is:
>
> Under what condition and for what kind of signal x's do the DFT F1(v) and 
> sampled version of ordinary FT F3(v) equate? I want F1(v) and F3(v) to be 
> exactly the same... what conditions shall I impose?
>
> Thanks!

I have this diagram below which I think will help answer your question.

http://12000.org/my_notes/transforms/index.htm

Nasser