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From: Rune Allnor <allnor@tele.ntnu.no>
Newsgroups: comp.soft-sys.matlab,comp.dsp
Subject: Re: DFT the same as sampled Foureir transform?
Date: 24 May 2007 08:49:43 -0700
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On 24 May, 09:45, "Mike" <meathea...@gmail.com> wrote:
> Hi all,
>
> I have the following question regarding the relation between DFT and Foureir
> Transform.

Fourier. After Jean Baptiste Joseph Fourier. Read his biography

http://www-history.mcs.st-andrews.ac.uk/Mathematicians/Fourier.html

and maybe you get enough respect for him to spell his name correctly.

> 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).

Wrong. The DFT is not defined for a sequence of "possibly
infinite length." The DFT is defined for discrete-time sequences
of *finite* length.

> Also, for this sequence of signal,

What is a "sequence of signal"?

> I have an ordinary Foureir Transform
> F2(v), I guess it's called DTFT.

No, you don't. I have no idea what a "sequence of signal" is.
The Dirscrete-Time Fourier transform is defined for a discrete-
time sequence of *infinite* length.

> I plan to sample the F2(v) to obtain the discrete version of the F2(v) and
> call it F3(v).

No need to do that, the discrete-time signals are already
"sampled". Sampling is a way to convert from a contionuous-time
signal to a discrete-time signal. This can be done for signals
of either finite of (formally) infinite duration in time.

> 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?

There is an answer to such questions. Not the one you expect
or will be happy to hear, but an answer to questions such as
yours exists. Now, I took very great care to avoid "your
question" in the past sentence, because you don't have
the necessary basis to formulate the proper question.
Before asking again, take your time to read up on, and
contemplate, the different variations of the Fourier transform.

You will have four cases to consider:

1) Countinuos time, infinite duration
2) Continuous time, finite duration
3) Discrete time, infinite duration
4) Discrete time, finite duration

Once you have done that, you will be able to formulate
a question which makes sense and, consequently, can be
answered in a meaningful way.

Rune