Insensitivity of the human ear to phase.

The human ear is insensitive to phase in the Fourier expansion of a periodic waveform: given a periodic signal [math]A_0/2+\sum\limits_{n=0}^{+\infty}A_n\cos(nt+\phi_n)[/math], we can replace it with [math]A_0/2+\sum\limits_{n=0}^{+\infty}A_n\cos(nt+\tilde\phi_n)[/math], where we changed the phase angles [math]\phi_n[/math] with randomly chosen [math]\tilde\phi_n[/math]. The two waveforms are possibly very different, but sound exactly the same!

 

Sisto Baldo

 
Resource Type
Activity
Tags
angle  ear  fourier  human  phase  series 
Target Group (Age)
19+
Language
English (United States)
 
 
GeoGebra version
4.4
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