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Subject: How to zoom into a certain part of FFT?
Date: Tue, 26 Jun 2007 20:06:00 -0700
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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!