Re: Extract Coefficients of Fourier Series

*To*: mathgroup at smc.vnet.net*Subject*: [mg58822] Re: Extract Coefficients of Fourier Series*From*: Peter Pein <petsie at dordos.net>*Date*: Wed, 20 Jul 2005 00:29:21 -0400 (EDT)*References*: <dbie2e$brj$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

mchangun at gmail.com schrieb: > Hi All, > > I have a set of points which have I fitted to a fourier serires with > the TrigFit function. This gives me a fourier series. What I want is > to extract all the coefficients of the series, square them, then sum > them. How do I this (more specifically, the extraction step? > > Thanks in advanced. > In[1]:= data = Table[4*x*(1 - x), {x, 0, 1, 1/1000}]; tf = TrigFit[data, 3, {x, 0, 1}] Out[2]= 0.666 - 0.40609304265918433*Cos[2*Pi*x] - 0.10152126067464604*Cos[4*Pi*x] - 0.04511907883733167*Cos[6*Pi*x] + 0.0012745085996715144*Sin[2*Pi*x] + 0.0006372480229067737*Sin[4*Pi*x] + 0.0004248250408689751*Sin[6*Pi*x] In[3]:= Cases[tf, a_?NumberQ | a_.(_Cos | _Sin) :> a, 1] Out[3]= {0.666, -0.40609304265918433, -0.10152126067464604, -0.04511907883733167, 0.0012745085996715144, 0.0006372480229067737, 0.0004248250408689751} In[4]:= %.% Out[4]= 0.6208120678738216 I splitted the instructions for easy verifying, the whole thing would be written in one function: coeffSqSum[tf_]:= Plus@@Cases[tf, a_?NumberQ | a_.(_Cos | _Sin) :> a^2, 1]; Leave the altenative a_?NumberQ out if you don't want the contant term squared & added. -- Peter Pein Berlin http://people.freenet.de/Peter_Berlin/