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Re: Quantifying Spectro-temporal Complexity


For a single sound, what I do is measure the average spectrum over time
and the rms amplitude vs. time. Then I construct a time-varying spectrum
whose components have the same frequencies but whose amplitudes vary
proportionally to the rms amplitude, while retaining the original rms
amplitude vs. time. I then measure the time-rms difference between the
original time-varying spectrum and the constructed one, normalized by
the time-rms of the rms amplitude. This is a measure of "spectral flux"
with values between from 0 to 1. If the spectrum is static and only
varies in amplitude, the measure gives zero. If the spectrum is dynamic
in that components are not well correlated, the result will be greater
than zero according to the degree of incoherence. Uncorrelated randomly
varying component amplitudes should give the highest value. I tried this
on a number of musical instrument sounds, and it seems to work. I have
not tried it on polyphonic sounds. Keep in mind that any measure like
this is contrived and needs to be somehow compared to the perception of
complexity, if that's even possible. Also, time-varying frequencies
should be considered.

Jim Beauchamp
Univ. of Illinois at Urbana-Champaign

You wrote:
>From: Nikolas Alejandro Francis <nfu@xxxxxxx>
>Date:         Wed, 27 Jul 2005 21:25:10 -0400
>To: AUDITORY@xxxxxxxxxxxxxxx
>Subject:      Quantifying Spectro-temporal Complexity
>Hello Everyone,
>I just joined this list and look forward to participating in new discussions.
>My question is if anyone is aware of a method for quantifying the
>spectro-temporal complexity of a set of sounds.  In the past I've moved a
>sliding window independently across time and frequency from 0 to the length of
>the sound and up to 22khz. For each window I found the standard deviation (SD)
>from the mean value within that window, and then averaged all of the SDs for
>all frequency and time windows, independently.  For each sound, I found the
>mean of all the SDs for frequency and time, resulting in a spectral complexity
>value and a temporal complexity value.  Finally I found the mean of these two
>values for an overall spectro-temporal complexity value.
>Does this sound sufficient?  Thanks.
>-Nik Francis