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From: "Vista" <abc@gmai.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 20:44:57 -0700
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Hi folks,

This is not a joke post. I really have this question in my mind for long 
time.

When I truncate/extract out F(w) for w in [-B, B] and use step size deltaB 
to sample it and then do IFFT, what is the portion of f(t) I see? Say f(t) 
for t in [a, b]. What are a and b?

Now suppose I find there is some fine structure in [c, d], which is shown 
from the visual display of f_hat(t), t in [a, b]. And a<c<d<b.

How to do IFFT targeting at f(t) on [c, d] with higher resolution?

And so on and so forth?

Thanks!


"Vista" <abc@gmai.com> wrote in message 
news:f5sk5g$qmm$1@news.Stanford.EDU...
> Hi all,
>
> 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?
>
> If I want to zoom into a certain part of f(t), how can I use inverse FFT 
> to do that?
>
> Let's say I only need [a, b] where 0<a<b< infinity, in the time domain,
>
> I only need to visualize the f(t), for t in [a, b],
>
> how do I sample F(w) and do the inverse FFT?
>
> -------------------------
>
> More generally, I am actually thinking of desing a "spectrum analyzer" 
> with zoom-in feactures:
>
> as you can see, first do a coarse level inverse FFT to gain a big picture 
> of the f(t) curve, and then allow user to zoom into a particular part of 
> the f(t) curve and display it with higher resolution of IFFT.
>
> How to do all of these?
>
> Thanks a lot!
>