Re: how to measure entropy of music?

From: Andor (an2or_at_mailcircuit.com)
Date: 12/04/04 

Date: 4 Dec 2004 01:28:10 -0800

glen herrmannsfeldt wrote:

> I would think a pure sine wave should be low complexity, so maybe
> you should compress the Fourier transform.

I think a vocoder does something similar: linear predictive coding
tries to fit an AR model to the input, effectively searching for the
formants (resonant peaks) of the "vocal tract" transfer function. If
you initialize an IIR filter with the LPC coefficients and the states
(delays) with the signal, you can let it "ring" like an oscillator -
the output will converge to a sum of pure damped sine waves at the
estimated frequencies of the formants. However, instead of storing the
sine waves, the vocoder stores the LPC coefficients and the residue
(prediction error).

To take this back to entropy, the energy of the prediction error could
well be regarded as the entropy of a vocal signal - it gives a good
measure on how unexpected the signal is, given its past history.

Recent work has shown that this method is also suited for general
audio signals, not just speech. The order of the AR model just
increases drastically (for interpolation, orders of 1000 - 3000 are
used). The same applies here for the prediction error and the entropy.

> Has anyone ever done an FFT of a whole CD?

If you take a music CD, I would expect a linear trend of the form
1/f^a. This is a common model for music signals, and it agrees well
with findings of long-range correlated time series.

For speech, I would guess a rectangular pulse response. The formants
vary across a certain frequency range, but are limited from above and
below.

>
> -- glen

Regards,
Andor

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