well, i remember a paper from long ago from James Beauchamp where he defines
spectral centroid as
�
� SUM{ |c_n| n } / SUM{ |c_n| }
�
where c_n is the complex Fourier coefficient for the nth harmonic. �if you
wanted to base it on
energy
�
� SUM{ |c_n|^2 n } / SUM{ |c_n|^2 }
�
it will give you the harmonic number (in fractional form) where the centroid of
magnitude or magnitude-squared (which is energy) is.
note that this expression is independent of the fundamental frequency, f0.
�
�
---------------------------- Original Message
----------------------------
Subject: [music-dsp] Cheap spectral centroid recipe
From: "Evan Balster" <e...@imitone.com>
Date: Mon, February 1, 2016 1:41 pm
To: music-dsp@music.columbia.edu
--------------------------------------------------------------------------
>
> First posting here. I'm an outsider to the DSP world, but I do quite a lot
> of DSP research and development. In the course of my work I have turned up
> a number of simple tricks which I imagine would prove handy to other
> developers. I have combed through a handful of classic music-dsp
> discussions (eg. pink noise generation) and I get the idea that sharing
> techniques is encouraged here -- so I would like to make a habit of doing
> this.
>
>
> 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, I can't find any mention of this trick online -- the
> literature almost always prescribes FFT.
>
> 1. Apply a first-difference filter to input signal A, yielding signal B.
> 2. Square signal A, yielding signal AA; square signal B, yielding signal
> BB.
> 3. Apply a low-pass filter of your choice to AA, yielding PA, and BB,
> yielding PB.
> 4. Divide PB by PA, then multiply the result by the input signal's
> sampling rate divided by pi.
>
i *think* what that will get you is
� SUM{ |c_n|^2 f0^2 n^2 } / SUM{ |c_n|^2 }
�
and it will be proportional to the square of frequency. �is that what
you want?
�
what if the first-difference filter (which is + 6 dB/oct) was replaced
by an inverse pinking filter (which is +3 dB/oct) and you did that? �then the
centroid measure would be proportional to frequency but still be based on
energy. �you would still have to divide by f0 (requiring a pitch
detector) to make it independent of the fundamental frequency and dependent
only on the waveshape.
�
> [example code] <http://pastebin.com/EfRv4HRC>
>
�
i'll look at it.
thanks Evan.
--
�
r b-j � � � � � � � � � r...@audioimagination.com
�
"Imagination is more important than knowledge."
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