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From:  NZTideMan <mulgor@gmail.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: Wed, 27 Jun 2007 05:11:23 -0000
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On Jun 27, 3:49 pm, "Ron N." <rhnlo...@yahoo.com> wrote:
> 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

What you're doing is "band-pass filtering".
You'll need to take the sqrt because a spectrum is energy, but you
want amplitude for the ifft.
But the spectrum contains no information on phase, so what are you
going to do about that?
Also, you must be aware that you'll have problems with Gibb's
phenomenon which causes "ringing" in the inverse Fourier transform.
To avoid that you'll need to smoothly taper the spectral cutoffs - I
use a tanh function for this.