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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 09:56:49 -0700
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"Nasser Abbasi" <nma@12000.org> wrote in message 
news:Zlc5i.36415$AR3.18889@newsfe07.phx...
>
> "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


Thanks Nasser!