Re: 1/f spectra

[Brian Gygi <bgygi@xxxxxxxxx>]

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.

and

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.

Brian

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