Re: 1/f spectra

[Nachum Ulanovsky <nachumu@xxxxxxxxxxxxx>]

Dear Jan,
The 1/f dependence is usually shown not for spectra of
original sounds, but for spectra of filtered sound envelopes.
This means that sounds are usually band-pass filtered, and
the output is squared and low-pass filtered -- and then
the spectra are computed for these fluctuations.
This is true for the studies by Voss & Clarke (1975; see refs
below) and Attias & Schreiner (1997). In fact, Voss & Clarke
(the "classic paper" you mentioned) explicitly write re
the audio signal from J.S.Bach's 1st Brandenburg concerto:
"The spectrum consists of a series of sharp peaks in the
frequency range 100Hz-2kHz corresponding to the individual
notes in the concerto and, of course, is not 1/f-like".
(see their Fig. 1a).
The 1/f dependence of spectra of envelope fluctuations
(or approximate 1/f dependence in Attias & Schreiner)
is shown for low frequencies only (below 100 Hz or so).

If you are interested in spectra of original sounds, you
can see examples in Dusenbery (1992; see his Fig. 9-5,
which is replotted from Waser & Brown 1986), which shows
average spectra of environmental soundscapes. The spectra
of such soundscapes are typically decreasing up to ~1kHz
or so, and then start to flatten. These spectra often have a
prominent peak around ~3-7 kHz, which is due to bird
calls. We have recently also analyzed a set of environmental
soudscapes (source: Cornell Library of Natural Sounds), and
obtained very similar results to Waser & Brown (1986).

Hope this helps,

Nachum Ulanovsky



REFERENCES:

Attias, H. & Schreiner, C. Low-order temporal statistics of
natural sounds. in Advances in Neural and Information
Processing Systems Vol. 9 (1997).

Dusenbery, D.B, Sensory Ecology (Freeman, New York 1992).

Voss, R. F. & Clarke, J. 1/f noise in music and speech.
Nature 258, 317-318 (1975).

Waser, P.M. and Brown, C.H., Habitat acoustics and primate
communication, Am. J. Primatol. 10, 135-154 (1986).



----------------------
Nachum Ulanovsky
Dept of Neurobiology, Hebrew University, Jerusalem, Israel
Phone: +972-2-6586363, Fax: +972-2-6586077
e-mail: nachumu@md.huji.ac.il
http://music.ls.huji.ac.il/members/nachum