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My question is how to determine the parameters of a signal from a spectrogram statistically. The most important parameters that I am looking for are the lower and higher frequencies of the signal. I have hundreds of these audio clips and I would like to perform statistics on them to determine the bandwidth of the signal. What is the best method to use to obtain these values statistically?

Find attached an audio clip and the label of signal that I am trying to analyse.
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  • $\begingroup$ Do you have bounding boxes or did you draw those for illustration only? $\endgroup$
    – Engineer
    Nov 15 '20 at 16:50
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    $\begingroup$ hey! you'll first need to define what "bandwidth" means to you; there's as many different sensible definitions of that as there are applications for the term, and you can't put the word "bandwidth" to anything without picking a definition that makes sense to what you'll be doing with it. $\endgroup$ Nov 15 '20 at 17:09
  • $\begingroup$ @MarcusMüller I wonder where this comment was some weeks earlier. $\endgroup$ Nov 16 '20 at 2:57
  • $\begingroup$ @Engineer no I added the boxes myself such that I could show what signal I am referring to. $\endgroup$
    – suyol854
    Nov 16 '20 at 9:57
  • $\begingroup$ @MarcusMüller I am trying to find the frequency content of the whistle. I have attached an image of the whistle spectrum where I have labelled the frequencies that I am trying to obtain. As I have said I am not trying to obtain these for one whistle but I would like to statistically obtain these values for a large values of whistles. $\endgroup$
    – suyol854
    Nov 16 '20 at 10:08
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A spectrogram is a tool to analyze non-stationnary signals, and hopefully identify or separate it onto simpler sources. Hence, parts of the spectrograms ought to be "different". Hence, from a statistical point of view, the 2D data is likely to be multimodal, and global statistical measures are likely to be useless.

If you now focus on specific "modes", like identifiable whistles in boxes, then you can retrieve 2D statistical spectral moments from those patches. These could be a 2D center of mass (in time and frequency) and the corresponding 2D spread (equivalent to a standard deviation) that would form an ellipsis around the center of mass. The vertical axis could provide an idea of the frequency span of this mode.

From my experience, this often requires to look at other statistical moments for more robustness.

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  • $\begingroup$ Thanks @LaurentDuval for your comment. I have shown the audio clip is a spectrogram form such that I could have a visual representation of my audio file which is easy to understand. I have large datasets of these whistles and I am trying to obtain parameters about the whistle such as the lower frequency and high frequency content of the whistle. I would then use this information to write an algorithm to search for the peaks between these frequencies. I have attached some images of the spectrum to my question. $\endgroup$
    – suyol854
    Nov 16 '20 at 10:01
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    $\begingroup$ @suyol854 you really need to try to be strict when defining terms like "lower frequency": What makes sometghing the "lower frequency"? Can you come up with a signal description? $\endgroup$ Nov 16 '20 at 11:31
  • $\begingroup$ @MarcusMüller Thank you for your comment high appreciated. Can you please guide me what do you mean by signal description and how it could be obtained, since I do not know what is the mathematical representation of the signal. I would have to deduce that from the recordings that I have. $\endgroup$
    – suyol854
    Nov 16 '20 at 11:52
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    $\begingroup$ I mean, you have something specific in mind when you say "lower frequency". Can you maybe describe what that is, with your spectrogram or PSD plots? $\endgroup$ Nov 16 '20 at 11:59

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