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Re: 1/f spectra

Hi Jan:

I don't know the Science paper you refer to, but there have been a few studies on the spectra on natural sounds:.  The problem is the particular setting or corpus of sounds surveyed will affect the results.

Hodgson, M. R., Rempel. R.& Kennedy, S. (1997).  “Measurement and prediction of typical speech and backgroundnoise levels in university classrooms during lectures,” J. Acoust. Soc. Am. 105(1), 226-233.


Hoth, D.F. (1941).  “Room noise spectra at subscriber’s telephone locations,”  J. Acoust. Soc. Am. 12, 499-504.

looked at classroom and offices, respectively, and generally found that the spectrum of summed background sounds rolls off (declines in amplitude) according to a 1/f function, somewhat similar to pink noise. 

However, in Gygi, B., Kidd, G. R. and Watson, C. S. "Spectral-temporal factors in the identification of natural sounds", to be published in JASA in Jan/Feb., I summed 100 environmental sounds and found that the long-term spectrum had slightly less than a 1/f slope, possibly due to the inclusion of a number of impact sounds that had high frequency transients. 

In general, in

Attias, H. &  Schreiner, C. E. (1997). “Temporal loworder statistics of natural sounds”. In Advances in Neural Info Processing Systems, 9, edited by M. Mozer (MIT Press, Cambridge, MA), pp 27-33.

the authors examined low-order statistics for speech, environmental sounds and music gathered from samples on CD sound effects.  They found that the power spectra rolled off according to a modified power law:    
S(T) = 1/(T02 + T2)"/2
where S(T) is the amplitude of the spectrum at frequency T, " ranges from 1.0-2.5, and T0 specifies the  f at which the rolloff begins.  The rolloff value is higher for speech than music or environmental sounds.  Note that the 1/f spectral rolloff mentioned above is a special case of this general law.

I hope this helps.


At 06:29 PM 11/14/2003 +0000, Jan Schnupp wrote:
Dear List,

I have heard it said on a number of occasions that 1/f spectra are very
commonly encountered among natural signals, and one might perhaps expect
the auditory system to reflect this fact in its design
(perhaps the fact that auditory filters get wider at higher CF and are
approximately logarithmically spaced is a simple relfection of the 1/f
nature of many sounds?)
However, I don't know ANY literature that discusses this 1/f phenomenon. I
seem to remember somebody mentioning at a conference that there is a
"classic" Science paper that marks the "discovery of the 1/f phenomenon".
If that is the case, I'd love to know the citation for it. Any other
references for other (particularly recent!) work relating to 1/f and it's
role in audition would of course also be very welcome. (Even better would
be pdf files of relevant papers, if anyone has any).

Thank you very much in advance for your help,

Jan Schnupp
Dr. Jan Schnupp
University Laboratory of Physiology
Parks Road, Oxford OX1 3PT, UK
Tel: +44-1865-272513  Fax: +44-1865-272469
E-mail: jan.schnupp@physiol.ox.ac.uk