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From:  Luna Moon <lunamoonmoon@gmail.com>
Newsgroups: comp.dsp,comp.soft-sys.matlab
Subject: Re: how to use IFFT to reconstruct signal in a specific region t in [a, b]?
Date: Sat, 11 Aug 2007 12:45:50 -0700
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On Aug 9, 8:43 am, julius <juli...@gmail.com> wrote:
> On Aug 8, 11:19 pm, "Luna Moon" <lunamoonm...@gmail.com> wrote:
>
> > Hi all,
>
> > Let's say by doing IFFT on F(v), which is the spectrum of signal f(t), I was
> > able to reconstruct f(t), for t in [0, T].
>
> > Now I want to ask is there a way to do another IFFT to reconstruct the
> > specific part f(t) for t in [T, 2T], without any waste of previous
> > calculations?
>
> > Basically, I want to ask, if it is possible to use IFFT to reconstruct to
> > any slot t in [a, b] in the time domain for signal f(t)?
>
> > Thanks a lot!
>
> You can use the Discrete Fourier Transform (DFT) to do it.
> By definition, the FFT is restricted to the "Fast" version of
> the DFT.
>
> By the way, did you realize that relating a signal via the DFT
> or FFT implicitly assume periodicity in both time and frequency?
> I can't understand your notation, but if my guess is correct you
> will find that x[n] is periodic in N.  In your notation somehow
> you are using continuous time t, which is incorrect.
>
> I hate to nitpick, but these points can be important.
> Julius

thanks! Of course I realize that DFT/FFT assumes the signal is
periodic. My question is related to the window of one such period. Yes
DFT/FFT has a focal window, and everything outside this window is
assumed to be periodic extension of the content within this window.
But in a reconstruction of time-domain signal from spectrum using
Inverse FFT/DFT, what is the default focal window? And how do we shift
the focal window? Eventually I want to be able to slide the window
along all the time-domain signal and focus on one part of the signal
at a time.

How to do that? Thanks a lot!