Subject: Re: 1/f spectra From: Nachum Ulanovsky <nachumu(at)MD.HUJI.AC.IL> Date: Sun, 16 Nov 2003 15:56:46 +0200Dear 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(at)md.huji.ac.il http://music.ls.huji.ac.il/members/nachum