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From:  "Ron N." <rhnlogic@yahoo.com>
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: Tue, 26 Jun 2007 20:49:44 -0700
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On Jun 26, 8:06 pm, "Vista" <a...@gmai.com> wrote:
> 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?

In order to meaningfully sample F(w), you need to know
something about its smoothness, else your sample points
might fall into deep gaps in F(w), or some-such.

There may also be a theorem saying that the width of
some portion of a waveform in one domain is inversely
proportional to its width in the other domain.  The
smaller the wiggles in f(t) you want to see, the wider
you need to make [-B, B], which makes sense, since the
higher frequency components in F(w) are what produces
the densest small wiggles in f(t).

If you want a tiny enough window from an ifft (much
less than log(n) points), you might be better off
directly calculating a segment of the dft.


IMHO. YMMV.
--
rhn A.T nicholson d.0.t C-o-M