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From: "Steve Amphlett" <Firstname.Lastname@Where-I-Work.com>
Newsgroups: comp.soft-sys.matlab
Subject: Re: FFT of signal segments
Date: Mon, 20 Oct 2008 14:40:17 +0000 (UTC)
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"Dave Brackett" <davebrackett@hotmail.com> wrote in message <gdi2ve$cud$1@fred.mathworks.com>...
> Hi, I have written some code to do a FFT based on this example but with a Hann window:
> http://www.mathworks.com/support/tech-notes/1700/1702.html
> 
> I am basically doing a STFT (short time FT) and comparing frequencies and power over time. So I am splitting up a recorded signal into many segments and computing a FFT on each. 
> 
> The thing that I am finding curious though is that the more segments that I split the signal into, the greater the power in the FFT for each segment. Should this be the case? I would have thought the opposite should be observed because of the reduction in power that windowing causes.
> 
> Because I am using a Hann window, I have divided the FFT magnitude by 0.5 which is the coherent gain scaling factor.
> I could post my code here but as it is based on the example at the above link it probably would only serve to confuse. 
> 
> If someone could clarify what I should expect to see when splitting the signal into several segments as compared to 1 segment, with regards to the power, that would be useful. Thanks.

Your 0.5 will correct the amplitude.  For energy correction, use sqrt(3/8).  Most people would express the correction the other way up:

Multiply by 2 for amplitude, sqrt(8/3) for energy.