Re: 1/f spectra (Brian Gygi )

Subject: Re: 1/f spectra
From:    Brian Gygi  <bgygi(at)EBIRE.ORG>
Date:    Fri, 14 Nov 2003 11:05:15 -0800

<html> <br> Hi Jan:<br><br> <font face="Times New Roman, Times" size=4>I don't know the Science paper you refer to, but there have been a few studies on the spectra on natural sounds:.&nbsp; The problem is the particular setting or corpus of sounds surveyed will affect the results.<br><br> Hodgson, M. R., Rempel. R.&amp; Kennedy, S. <b>(1997)</b>.&nbsp; “Measurement and prediction of typical speech and backgroundnoise levels in university classrooms during lectures,” J. Acoust. Soc. Am. <b>105</b>(1), 226-233.<br><br> and<br><br> Hoth, D.F. <b>(1941)</b>.&nbsp; “Room noise spectra at subscriber’s telephone locations,”&nbsp; J. Acoust. Soc. Am. <b>12</b>, 499-504.<br><br> 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/<i>f</i> function, somewhat similar to pink noise.&nbsp; <br><br> However, in Gygi, B., Kidd, G. R. and Watson, C. S. &quot;Spectral-temporal factors in the identification of natural sounds&quot;, 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/<i>f </i>slope<i>, </i>possibly due to the inclusion of a number of impact sounds that had high frequency transients.&nbsp; <br><br> In general, in <br><br> Attias, H. &amp;&nbsp; Schreiner, C. E. <b>(1997)</b>. “Temporal loworder statistics of natural sounds”. In <i>Advances in Neural Info Processing Systems</i>, <b>9</b>, edited by M. Mozer (MIT Press, Cambridge, MA), pp 27-33.<br><br> the authors examined low-order statistics for speech, environmental sounds and music gathered from samples on CD sound effects.&nbsp; They found that the power spectra rolled off according to a modified power law:&nbsp;&nbsp;&nbsp;&nbsp; <br> <div align="center">S(</font><font face="WP Greek Century" size=4>T</font><font face="Times New Roman, Times" size=4>) = 1/(</font><font face="WP Greek Century" size=4>T</font><font face="Times New Roman, Times" size=2><sub>0</sub><sup>2</sup></font><font face="Times New Roman, Times" size=4> + </font><font face="WP Greek Century" size=4>T</font><font face="Times New Roman, Times" size=2><sup>2</sup></font><font face="Times New Roman, Times" size=4>)</font><font face="WP Greek Century" size=2><sup>&quot;</font><font face="Times New Roman, Times" size=2>/2<br> </sup></font></div> <font face="Times New Roman, Times" size=4>where S(</font><font face="WP Greek Century" size=4>T</font><font face="Times New Roman, Times" size=4>) is the amplitude of the spectrum at frequency </font><font face="WP Greek Century" size=4>T</font><font face="Times New Roman, Times" size=4>, </font><font face="WP Greek Century" size=4>&quot;</font><font face="Times New Roman, Times" size=4> ranges from 1.0-2.5, and </font><font face="WP Greek Century" size=4>T</font><font face="Times New Roman, Times" size=2><sub>0</sub></font><font face="Times New Roman, Times" size=4> specifies the&nbsp; <i>f</i> at which the rolloff begins.&nbsp; The rolloff value is higher for speech than music or environmental sounds.&nbsp; Note that the 1/<i>f</i> spectral rolloff mentioned above is a special case of this general law.<br><br> </font>I hope this helps.<br><br> Brian<br><br> At 06:29 PM 11/14/2003 +0000, Jan Schnupp wrote:<br> <blockquote type=cite class=cite cite>Dear List,<br><br> I have heard it said on a number of occasions that 1/f spectra are very<br> commonly encountered among natural signals, and one might perhaps expect<br> the auditory system to reflect this fact in its design<br> (perhaps the fact that auditory filters get wider at higher CF and are<br> approximately logarithmically spaced is a simple relfection of the 1/f<br> nature of many sounds?)<br> However, I don't know ANY literature that discusses this 1/f phenomenon. I<br> seem to remember somebody mentioning at a conference that there is a<br> &quot;classic&quot; Science paper that marks the &quot;discovery of the 1/f phenomenon&quot;.<br> If that is the case, I'd love to know the citation for it. Any other<br> references for other (particularly recent!) work relating to 1/f and it's<br> role in audition would of course also be very welcome. (Even better would<br> be pdf files of relevant papers, if anyone has any).<br><br> Thank you very much in advance for your help,<br><br> Jan Schnupp<br> Dr. Jan Schnupp<br> University Laboratory of Physiology<br> Parks Road, Oxford OX1 3PT, UK<br> Tel: +44-1865-272513&nbsp; Fax: +44-1865-272469<br> E-mail: jan.schnupp(at)<br> </blockquote></html>

This message came from the mail archive
maintained by:
DAn Ellis <>
Electrical Engineering Dept., Columbia University