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From:  julius <juliusk@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: Thu, 09 Aug 2007 12:43:02 -0000
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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