source file: m1547.txt Date: Wed, 7 Oct 1998 17:21:26 -0400 Subject: RE: Cancelling out beats From: "Paul H. Erlich" I wrote, >> Paul H., the nonlinear processing that the ear does actually increases >> the frequency resolution over what the standard uncertainty relation >> would give for an analyzer with the ear's temporal resolution, thus >> decreasing (rather than creating) the incidence of beats. Paul H. wrote, >?? I must be misunderstanding something. If you analyze the signal >using a process which decomposes it linearly, such as a Fourier >transform, no energy is detected at the beat frequency. What is a >decrease from nothing? I think this is what Gary Morrison was talking >about when he said (talking about bram's beat-canceling idea): You are correct only with an infinitely long sampling window. The temporal resolution of the ear is far better than that, on the order of several milliseconds. Standard signal processing theory says that the temporal resolution times the frequency resolution is greater than 1 or 2*pi or some such constant. The ear beats this by performing several layers of processing, which is what I refer to as "nonlinear".