Path: news.mathworks.com!newsfeed-00.mathworks.com!newscon02.news.prodigy.net!prodigy.net!news.glorb.com!sn-xt-sjc-05!sn-xt-sjc-09!sn-post-sjc-01!supernews.com!news.supernews.com!not-for-mail
From: Randy Yates <yates@ieee.org>
Newsgroups: comp.soft-sys.matlab,comp.dsp
Subject: Re: DFT the same as sampled Foureir transform?
Date: Thu, 24 May 2007 13:23:09 -0400
Organization: The Universal Church of Christ
Message-ID: <m3lkferv9e.fsf@ieee.org>
References: <f33fqk$2f8$1@news.Stanford.EDU> <1180021783.330512.237760@w5g2000hsg.googlegroups.com> <f34g2p$qra$1@news.Stanford.EDU> <m37iqydu5z.fsf@ieee.org>
User-Agent: Gnus/5.1007 (Gnus v5.10.7) XEmacs/21.4.20 (linux)
Cancel-Lock: sha1:dK3q7sVCaM+rwmr+odp392tvmV0=
MIME-Version: 1.0
Content-Type: text/plain; charset=us-ascii
X-Complaints-To: abuse@supernews.com
Lines: 40
Xref: news.mathworks.com comp.soft-sys.matlab:410877 comp.dsp:222982



Randy Yates <yates@ieee.org> writes:

> "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.

PS: You probably meant to label the sequences x0, x1, ..., x(n-1), making
n samples.
-- 
%  Randy Yates                  % "Remember the good old 1980's, when 
%% Fuquay-Varina, NC            %  things were so uncomplicated?"
%%% 919-577-9882                % 'Ticket To The Moon' 
%%%% <yates@ieee.org>           % *Time*, Electric Light Orchestra
http://home.earthlink.net/~yatescr