Path: news.mathworks.com!newsfeed-00.mathworks.com!newsfeed2.dallas1.level3.net!news.level3.com!postnews.google.com!h2g2000hsg.googlegroups.com!not-for-mail
From: Andor <andor.bariska@gmail.com>
Newsgroups: comp.soft-sys.matlab,comp.dsp
Subject: Re: DFT the same as sampled Foureir transform?
Date: 24 May 2007 02:21:55 -0700
Organization: http://groups.google.com
Lines: 41
Message-ID: <1179998515.753120.45840@h2g2000hsg.googlegroups.com>
References: <f33fqk$2f8$1@news.Stanford.EDU>
NNTP-Posting-Host: 83.77.240.175
Mime-Version: 1.0
Content-Type: text/plain; charset="us-ascii"
X-Trace: posting.google.com 1179998519 23492 127.0.0.1 (24 May 2007 09:21:59 GMT)
X-Complaints-To: groups-abuse@google.com
NNTP-Posting-Date: Thu, 24 May 2007 09:21:59 +0000 (UTC)
In-Reply-To: <f33fqk$2f8$1@news.Stanford.EDU>
User-Agent: G2/1.0
X-HTTP-UserAgent: Mozilla/4.0 (compatible; MSIE 6.0; Windows NT 5.1),gzip(gfe),gzip(gfe)
X-HTTP-Via: 1.0 SERVER
Complaints-To: groups-abuse@google.com
Injection-Info: h2g2000hsg.googlegroups.com; posting-host=83.77.240.175;
Xref: news.mathworks.com comp.soft-sys.matlab:410796 comp.dsp:222954



Mike wrote:
> Hi all,
>
> I have the following question regarding the relation between DFT and Foureir
> Transform.

Your misspelling is too consistent to by a typo. The guy's name was
Fourier!


> 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).

You are mixing up all kinds of objects here.

For infinite length sequences that are square-summable and represent
evenly sampled bandlimited finite-energy signals, you can use the DTFT
(if it converges), or the z-transform. For periodic, discrete and
infinitely long sequences the z-transform doesn't converge, and you
need the DFS (discrete Fourier series).

For finite length vectors, you can use the DFT (discrete Fourier
transform). The DFS and the DFT are closely related.

There are infinitely many distinct sequences x[n] with DTFT X(w) where
the inverse DFT y of the unifomly sampled DTFT, namely

y = IDFT{ X(2 pi k/N) }, k=0,1,...,N-1,

are all equal. For some of them, you have y[n] = x[n], n=0,1,...,N-1,
for others you don't.

Did this help?

Regards,
Andor