I looked over the other entries regarding peak detection and none seem to answer my question.

I'm working with Fourier spectra of digitized audio that can't be measured again. There are no constraints on the nature of the audio.

Finding outliers is easy. I'm worried about "fat" peaks whose contours might be made jagged by background noise. Their "summits" are peaks among peaks. So how salient and separate does a peak need to be in order to qualify?

Is there a statistical way of approaching the problem? I could do something ad hoc, but without firm theoretical grounding, I rely much more on testing to confirm the algorithm's robustness. I'd like to know theoretically, rather than empirically, that my algorithm is sound.

Also, for those who have read this far, is there a good corpus of audio test data I can use for analysis algorithms?

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    $\begingroup$ Needed is your definition of when a peak is not a peak. For what reasons aren't you considering all peaks to be peaks? $\endgroup$ – hotpaw2 Mar 21 '14 at 21:20
  • $\begingroup$ I'm realizing that my question is poorly conceived. Should I just go ahead and delete it? $\endgroup$ – MackTuesday Mar 21 '14 at 21:26
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    $\begingroup$ MackTuesday, do you have data you can put up, as say, a .mat file? $\endgroup$ – Tarin Ziyaee Mar 22 '14 at 14:17
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    $\begingroup$ mack, it's not an illegit question. i'm curious about "Fourier spectra of digitized audio that can't be measured again". but you still have access to the original audio, no? how is the spectra computed? is not the audio windowed before going into the FFT? knowing the nature of that window will tell you alot about the nature of the peaks. $\endgroup$ – robert bristow-johnson Mar 22 '14 at 15:32
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    $\begingroup$ @MackTuesday So something like this perhaps? PS: You have to put an @ symbol before my name so that I know you have replied. $\endgroup$ – Tarin Ziyaee Mar 23 '14 at 0:37

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