Path: utzoo!utgpu!jarvis.csri.toronto.edu!mailrus!wuarchive!cs.utexas.edu!uunet!crdgw1!ge-dab!sunny!harrison
From: harrison@sunny.DAB.GE.COM (Gregory Harrison)
Newsgroups: comp.dsp
Subject: Re: FFT Window Effects
Message-ID: <2615@ge-dab.GE.COM>
Date: 9 Nov 89 15:25:57 GMT
References: <2564@radio.oakhill.UUCP>
Sender: news@ge-dab.GE.COM
Reply-To: harrison@sunny.UUCP (Gregory Harrison)
Organization: GE Simulation & Control Systems Dept., Daytona Beach, FL
Lines: 37

In article <2564@radio.oakhill.UUCP> charlie@oakhill.UUCP (Charlie Thompson) writes:
>window might affect the signal and noise power calculations.  Since
>the window 'smears' the harmonics into adjacent bins it must likewise
>do so to the noise bins...thus affecting the noise power calculation.

 Have you looked in "On the use of windows for harmonic analysis
with the discrete Fourier Transform"  Fredric J. Harris, Proc. IEEE
Vol. 66, No. 1, Jan 1978, pp. 51 to 83?   There are some reference
in there, in addition to the info in the main text.  

I thought that the smearing was due to the discontinuities at the
edges of the input time series, and that the window is applied
in an attempt to decrease the smearing, as opposed to causing it.

Are you looking for distortion due to quantization, or due to 
other signal energy in the input signal.

A good book illustrating windowing, and a lot of other DSP info,
in very straightforward and computer based manner is
First Principles of Digital Signal Processing, by Strum and Kirk
~1988.  The book is at home, so this is from memory.  

Possibly a good method to get a close approximation to the noise would 
be to take the FFT of the signal, go in and set the frequency components
(bins) immediately around the sine wave peak to zero for both 
positive and negative components.  Then apply Parseval's Theorem
on the remaining frequency components.  In other words, sum up the 
squares of the remaining components to get the total noise power in the 
spectrum.  If the noise power is much lower than the sine wave, I would
think that a good approximation to the noise power in the signal can be 
gained in this manner.  Assuming that the noise is aperiodic, and of low
amplitude, smearing due to discontinuities of the noise at the edges
of the input spectrum should be negligable in amplitude.  This may at
least provide a basis of comparison between input samples.

Greg Harrison
My opinions are not intended to express those of GE.