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?
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.