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From: "Paul Mennen" <nospam@mennen.org>
Newsgroups: comp.soft-sys.matlab
Subject: Re: how to reverse windowing effect?
Date: Tue, 20 May 2008 04:29:02 +0000 (UTC)
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"ggk giust" <ggkmath@comcast.net> wrote 
> I see a lot of 
> references to windowing in the literature, but no 
> information about how to reverse the effect of windowing 
> when going back from the frequency to the time domain. 

That's because it is not possible. Some operations, such as
the FFT for example do not destroy information and thus are
completely reversible. Other operations are not.

Consider an operation on a block of data where each point is
replaced with the average of the current point and the
previous point (i.e. blk(k) = (blk(k) + blk(k-1))/2.
(I sometimes call this the "1 1" filter). Clearly the result
is smoother than the input. Now would you expect this
operation to be reversible? ... I hope not :)

Windowing is much the same thing, and you can think of it as
a smoothing filter in the frequency domain. For instance the
Hanning window is a "1/4 1/2 1/4" filter in the frequency
domain. Regardless of whether you are smoothing in the
frequency domain or the time domain, information is lost and
you can't reverse the operation.

~Paul