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Re: [Discuss-gnuradio] FFT of FFTs

From: Frank Brickle
Subject: Re: [Discuss-gnuradio] FFT of FFTs
Date: Sun, 19 Jun 2005 02:31:22 -0400
User-agent: Mozilla/5.0 (X11; U; Linux i686; en-US; rv:1.4) Gecko/20030624

Eric Blossom wrote:

Once you've got your individual streams of signals, for each one I
would compute an estimate of whether it is occupied.

Good suggestions.

Elaborating on this a little, you might consider taking differences of successive magnitude or power spectra. If you're actually looking for periodicities in the onsets and releases, the resulting positive and negative pulses are very easy to track. This is a standard technique for first-order activity detection in spectral measurements.

Another productive technique is to take the wavelet transform of the magnitude, power, or difference spectrum, especially when the signals of interest are smeared over several bins. In this case you are looking for large wavelet coefficient magnitudes in the dilation region of the wavelet transform that corresponds to the spreading bandwidth in the original spectrum.

There is yet another arsenal of methods to throw at this problem if you are in a position to keep a full tableau of past spectra in three-dimensional form. For example, a conventional histogram equalization on such a tableau of past spectra is quite effective at bringing "activity stripes" out of the noise, and there is a robust likelihood score comparing before- and after-equalization densities. But that's really getting ahead of the subject...


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