Re: Extracting coefficients for sinusoidals

*To*: mathgroup at smc.vnet.net*Subject*: [mg60530] Re: [mg60477] Extracting coefficients for sinusoidals*From*: "W. Craig Carter" <ccarter at mit.edu>*Date*: Mon, 19 Sep 2005 04:45:47 -0400 (EDT)*References*: <200509170632.CAA16738@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

This works: f[x_] := a1*x + a1*x^2 + a1*x^3 + a4*x^4 + a5*x^5 signal = Sin[p] Coefficient[Expand[TrigReduce[f[signal]]],Sin[3 p]] is -a1/4 - 5 a5/16 and Coefficient[Expand[TrigReduce[f[signal]]],Cos[4 p]] is a4/8 On Sat, 17 Sep 2005, Helge Stenstrom wrote: > Date: Sat, 17 Sep 2005 02:32:01 -0400 (EDT) > From: Helge Stenstrom <helge.stenstrom at ericsson.com> To: mathgroup at smc.vnet.net > Subject: [mg60530] [mg60477] Extracting coefficients for sinusoidals > > Suppose I have a signal > signal = Sin[p] > > and a non-linear function > f[x_] := x - x^3/3 > > then > f[signal] = Sin[p] - Sin[p]^3/3 > > but I don't want this form (with powers of the Sin function), but > rather the form with multiples of p. TrigReduce can solve that: > > signal // f // TrigReduce > > (9*Sin[p] + Sin[3*p])/12 > > It's easy to extract the coefficients by visual inspection, > > 9/12, 1/12 > > but how can it be done programmaticaly? With a more complex non-linear > function, for example > > a1*x + a1*x^2 + a1*x^3 + a4*x^4 + a5*x^5 > using > signal // f // TrigReduce // InputForm > resulting in > (8*a1 + 6*a4 - 8*a1*Cos[2*p] - 8*a4*Cos[2*p] + 2*a4*Cos[4*p] + 28*a1*Sin[p] + > 10*a5*Sin[p] - 4*a1*Sin[3*p] - 5*a5*Sin[3*p] + a5*Sin[5*p])/16 > > visual ispection is no longer simple enough. So how can I get the > coefficients, individually or as a list? > > I'm not sure how I want the Cos and Sin terms to be treated; probably > a*Cos[x] should correspond to a*I*Sin[x] when the coefficients are > collected. > > -- > Helge Stenstr=F6m > > W. Craig Carter Lord Foundation Professor of Materials Science and Engineering MIT, Dept. of Materials Science and Engineering 13-5018 77 Massachusetts Ave, Cambridge, MA 02139-4307 USA 617-253-6048 ccarter at mit.edu http://pruffle.mit.edu/~ccarter http://pruffle.mit.edu/~ccarter/FAQS/ http://pruffle.mit.edu/~ccarter/I_do_not_use_microsoft.html

**References**:**Extracting coefficients for sinusoidals***From:*Helge Stenstrom <helge.stenstrom@ericsson.com>