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From:  John Hadstate <jh113355@hotmail.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 05:26:13 -0700
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On Jun 26, 11:06 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?
>

It depends on what you mean by "focus".  If you mean "set all the
unwanted spectral components to zero" and then you IFFT the result,
f_hat(nT) represents a filtered version of the original f(nT) over the
entire interval represented by the samples of f(nT).

If, by "focus", you mean "discard the unwanted spectral components"
and then you IFFT the result (containing a smaller number of spectral
components), f_hat(nT_prime) represents a decimated and filtered
version of the original f(nT), still over the entire interval
represented by the samples of f(nT).