Raised CosinesDate: 01/28/2001 at 19:26:55 From: Deborah Subject: Raised cosines Hi Dr. Math, Can you explain to me in the simplest way possible what raised cosines are and how they work? I am a biology student and I know basic single-variable calculus and elementary linear algebra. Thank you. Date: 01/29/2001 at 10:56:30 From: Doctor Douglas Subject: Re: Raised cosines Hi Deborah, I've come across "raised cosines" in the field of signal processing, where it is simply used to mean a sinusoidal function (a sine or cosine) that also has a constant, or an "offset" term: f(t) = C + A cos(wt) where C is a constant, and Acos(wt) is the usual sinusoidal part with which you're probably familiar (w is a kind of frequency, and is also a constant with respect to t). I think you won't have too much trouble using functions such as f(t), above - they're fairly easy to integrate and differentiate, for example: df/dt = -wA sin(wt) In a biological context, a set of such functions added together may give a person's blood pressure as a function of time. If we tried to model the pressure with just one f, as above, then the maximum pressure would be C+A (the systolic pressure) and the minimum would be C-A (diastolic pressure). Of course the actual pressure behavior is quite a bit more complicated that that given by a single raised cosine. It's also possible that "raised cosine" means something else entirely. If you find this to be the case, let us know! - Doctor Douglas, The Math Forum http://mathforum.org/dr.math/ |
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