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From: tohall@mars.lerc.nasa.gov (Dave Hall (Sverdrup))
Newsgroups: comp.dsp
Subject: Basic Question on Resolution of Spectral Analysis
Message-ID: <1991Feb22.235510.22045@eagle.lerc.nasa.gov>
Date: 22 Feb 91 23:35:43 GMT
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      Here is a fundamental question that has been giving me trouble in
a spectral analysis application of DSP:

    I need to analyze a signal that contains a "fundamental" tone at
about 3200 Hz (call this f0) plus "sidebands" located at f0 +/- 1 hz, 
f0 +/- 2 hz   .......    I am also interested in signals at 2f0 +/- 2 hz,
etc (harmonics of the tone cluster at f0). My analyszer will be set up
to digitize at 32 Khz with Low pass anti-aliasing filters at 10 Khz.

    My problem has to do with getting enough resolution in my discrete
Fourier transform to separate these closely spaced tones. The fundamental
resolution in the analysis is, I THINK:

      DELTA F =  FS / N,     where:   FS = sample rate
                                       N = number of samples



    OR:      N = FS / DELTA F

             N = 32 kHZ / 1 hZ   =   32 K SAMPLES!!!!


    This is a best case (minimum) number of samples assuming no "smearing"
due to windowing, etc. My problem lies in the area of manipulating arrays
in the 32K - 128K sample range, and trying to compute the FFT. I have
been trying various "zoom" analysis techniques described in the book 
"Signal Processing Algorithms" by Stearns abd David (Prentice Hall - 1988)
including the chirp z-transform. These techniques don't seem to do anything
to improve spectral resolution (ie- ability to separate closely spaced tones)
The bottom line resolution seems to always be set by the number of pts
in the original time-sample. "Zoom" techniques just seem to speed up the
analysis over a narrow portion of the spectrum, providing pretty plots
as well.

      This may sound like a dumb question, but is there some way to get 
the resolution I need without using such a huge ensemble? Any help would
be appreciated. 



          Thanks in Advance.

                   Dave Hall


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