Path: news.mathworks.com!newsfeed-00.mathworks.com!newsfeed2.dallas1.level3.net!news.level3.com!postnews.google.com!m36g2000hse.googlegroups.com!not-for-mail
From:  Oli Charlesworth <catch@olifilth.co.uk>
Newsgroups: comp.soft-sys.matlab,sci.math.num-analysis,comp.dsp,sci.math,sci.physics
Subject: Re: How to zoom into a certain part of FFT?
Date: Wed, 27 Jun 2007 00:14:12 -0700
Organization: http://groups.google.com
Lines: 27
Message-ID: <1182928452.919421.42850@m36g2000hse.googlegroups.com>
References: <f5sk5g$qmm$1@news.Stanford.EDU>
NNTP-Posting-Host: 81.102.137.54
Mime-Version: 1.0
Content-Type: text/plain; charset="us-ascii"
X-Trace: posting.google.com 1182928453 11898 127.0.0.1 (27 Jun 2007 07:14:13 GMT)
X-Complaints-To: groups-abuse@google.com
NNTP-Posting-Date: Wed, 27 Jun 2007 07:14:13 +0000 (UTC)
In-Reply-To: <f5sk5g$qmm$1@news.Stanford.EDU>
User-Agent: G2/1.0
X-HTTP-UserAgent: Mozilla/5.0 (X11; U; Linux i686; en-US; rv:1.8.1.2) Gecko/20061023 SUSE/2.0.0.2-1.1 Firefox/2.0.0.2,gzip(gfe),gzip(gfe)
Complaints-To: groups-abuse@google.com
Injection-Info: m36g2000hse.googlegroups.com; posting-host=81.102.137.54;
Xref: news.mathworks.com comp.soft-sys.matlab:415945 sci.math.num-analysis:97288 comp.dsp:224706 sci.math:1026409 sci.physics:1331515


On Jun 27, 4:06 am, "Vista" <a...@gmai.com> wrote:
> Hi all,
>
> Suppose I have a signal f(t), t is in [0, +infinity).
>
> And I have its spectrum F(w).
>
> Let's say I found out that its main spectrum has 99.9% in [-B, B].
>
> So I truncate/extract out the portion of F(w), for w in [-B, B], and
> discretized the interval into small grids with step size deltaB.
>
> And I then do the inverse FFT on the above samples of F(w), let's call the
> inverse FFT reconstruction f_hat.
>
> Which part of f(t) does this inverse FFT f_hat represent?

Just as sampling a non-bandlimited function in the time domain causes
time-domain aliasing, the dual occurs in your scenario.  You are
sampling a non-time-limited function in the frequency domain, which
will cause frequency-domain aliasing.


--
Oli