Although I’m still into the idea of having linear regression as a statistic in the toolbox (primarily for the R2 value you can get out of the algorithm), @tremblap re-iterated the usefulness of derivatives for getting some kind of summary of the morphology of a sound, particularly if you take >1 derivative.
After speaking @jamesbradbury about this a couple of weeks ago, I guess, mathematically speaking, you can’t have more derivatives than the amount of analysis frames you have, minus one. So if I’m dealing with the tiny windows (7 frames spread across 256 samples) I’m dealing with, particularly with spectral frames where I ignore the outer 4 frames, I’m realistically looking at only 3 analysis frames.
So my fundamental question is, is there some kind of ballpark ratio for how many derivatives you can have for any given amount of frames? So, if I have 7 analysis frames, is two derivatives “too much”? If I’m trying to get the most out of the morphology should I even do three derivatives?
Obviously I can, and will, do some testing with this, but the numbers that come out of the derivatives are a bit abstract, particularly for higher order ones. So it’s not as straight forward as doing it and looking at the numbers, since I wouldn’t really have an idea of what I’m looking at.
A side/sub-question here is to do with edge cases and derivatives. As mentioned above, I have a 256 sample window which I’m analyzing with
@fftsettings 256 64 512, which gives me 7 frames of analysis. For loudness, I analyze all 7, but for spectral shape, I do
@startframe 3 @numframes 3, giving me only the inner three frames. In my early tests I thought this gave me a better representation of what was in the overall analysis window.
Now, I will probably revisit this if/once we have some way to weigh the spectral descriptors by loudness, since I could be more confident that nothing would be over-represented (perceptually speaking) BUT I’m thinking of folding in more of the spectral frames if it turns out that higher order derivatives are, in fact, useful for small sample sets. As in, even if the centroid, for example, gets pulled around by the edge cases, that having a better morphological representation would offset that.
So a little bit of thinking out loud, but a bit more of asking a theoretical question on the usefulness of higher order derivatives on small time series. (lol, typing that out felt like a song chorus since its also the thread title)