Evan Balster wrote:
...
To that end: A handy, cheap algorithm for approximating the power-weighted
spectral
centroid -- a signal's "mean frequency" -- which is a good heuristic for
perceived sound
brightness <https://en.wikipedia.org/wiki/Brightness#Brightness_of_sounds>. In
spite of
its simplicity, ...
Hi,
Always interesting to learn a few more tricks, and thanks to Ethan's explanation I get
there are certain statistical ideas involved. I wonder however where those ideas in
practice lead to, because of a number of assumptions, like the "statistical variance" of a
signal. I get that a self correlation of a signal in some normal definition gives an idea
of the power, and that you could take it that you compute power per frequency band. But
what does it mean when you talk about variance ? Mind you I know the general theoretics up
to the quantum mechanics that worked on these subjects long ago fine, but I wonder what
the understanding here is?
Some have remarked about the analysis of a signal into ground frequency and harmonics that
it might be hard to summarize and make an ordinal measure for "brightness" as a one
dimensional quantity, I mean of you look at a number of peaks in a frequency graph, how do
you sum up the frequency of the signal, if there is one, and the meaning of the various
harmonics in the spectrum, if they are to be taken as a measure of the brightness? So a
trick is fine, though I do not completely understand the meaning of a brightness measure
for frequency analysis.
Of course to determine a statistical measure about a spectrum, either based on sampled
signals or (where the analysis comes from and is only generally correct for signal from -
to + inf) on a continuous signal, and based either on a Fourier integral/summation or a
Fast Fourier analysis (with certain analysis length and frequency bin accuracy), you could
use the general big numbers theorem and presume there's a mean and a variance. It would be
nice to at least make credible why this is an ok analysis, because a lot of signals are
far from Gaussian distributed in the sense of the frequency spectrum.
T.
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