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From: "Fred Marshall" <fmarshallx@remove_the_x.acm.org>
Newsgroups: comp.dsp,comp.soft-sys.matlab
References: <f9e4pe$klc$1@news.Stanford.EDU>
Subject: Re: how to use IFFT to reconstruct signal in a specific region t in [a, b]?
Date: Wed, 8 Aug 2007 22:59:48 -0700
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"Luna Moon" <lunamoonmoon@gmail.com> wrote in message 
news:f9e4pe$klc$1@news.Stanford.EDU...
> 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)?

The answer is: "it depends".

First of all, since you're doing an IFFT, the spectral information is given 
at discrete frequencies, the time series must be periodic. And, since the 
time sequence resulting is also discrete, the corresponding spectral 
sequence is periodic.

So, once you've done the IFFT, you have generated one period of a periodic / 
infinite time series.  After that, you should be able to figure out the 
values for any other time period ... but it's a bit of a trivial exercise 
when you know it's periodic isn't it?

In your opening description, you left out an important step:
In doing the IFFT, you generate a time sequence in [0,T] but have not yet 
reconstructed it on t (i.e. have not made it continuous which is usually 
what "reconstruction" means).

Proper reconstruction might use a Dirichlet kernel (which is periodic) - so 
once the reconstruction is done, you have the periodic f(t) for all t.

Fred