Re: RE: Fourier Series Expansions and it's Coefficients question revised tia

*To*: mathgroup at smc.vnet.net*Subject*: [mg85322] Re: [mg85293] RE: [mg85198] Fourier Series Expansions and it's Coefficients question revised tia*From*: DrMajorBob <drmajorbob at bigfoot.com>*Date*: Wed, 6 Feb 2008 01:24:16 -0500 (EST)*References*: <200802010720.CAA10016@smc.vnet.net> <13683770.1202246769990.JavaMail.root@m08>*Reply-to*: drmajorbob at bigfoot.com

Below I show a way to output a fit function and eliminate the error messages. I used a couple of tricks in NIntegrate; I'm not sure both are needed. Needs["FourierSeries`"] d = {14, 18.7, 9, 4.1, 6.7, 6, 6.3, 8.4, 4, 2.9, 14}; data = Thread[{Range@Length@d, d}]; f = Interpolation[data, PeriodicInterpolation -> True]; MapIndexed[{First@#2, #1} &, d] == MapIndexed[Reverse@Flatten@List[##] &, d] == data True nintegrate[expr_, {v_, lo_, hi_}] := With[{rnge = Flatten@{v, Range[lo, hi]}}, NIntegrate[expr, rnge, Method -> "LocalAdaptive"]] s[x_] = Chop[ FourierTrigSeries[f[x], x, 5, FourierParameters -> {-1, 1/10}] /. Integrate -> nintegrate] 8.01+ 1.24467 Cos[(\[Pi] x)/5] - 3.09947 Cos[(2 \[Pi] x)/5] - 2.72951 Cos[(3 \[Pi] x)/5] - 0.00418324 Cos[(4 \[Pi] x)/5] + 0.00868891 Cos[\[Pi] x] + 3.41712 Sin[(\[Pi] x)/5] + 3.05416 Sin[(2 \[Pi] x)/5] + 0.0107795 Sin[(3 \[Pi] x)/5] - 0.0314359 Sin[(4 \[Pi] x)/5] Show[Plot[s[x], {x, -10, 20}], Graphics@Point@data] Bobby On Tue, 05 Feb 2008 05:10:24 -0600, Jaccard Florian <Florian.Jaccard at he-arc.ch> wrote: > Hello! > > I looked at the answers you already got and tried them. > InterpolatingPolynomial is a good idea, but the difference with what you > expect it a bit too big. > The answer Dana gave was very good, but I'm afraid TrigFit doesn't > really exist anymore in version 6... > So I would do it like this, hoping it looks like you wish: > > d = {14, 18.7, 9, 4.1, 6.7, 6, 6.3, 8.4, 4, 2.9, 14}; > > f = Interpolation[d, PeriodicInterpolation -> True]; > > << "FourierSeries`" > > s[x_] = N[FourierTrigSeries[f[x], x, 5, FourierParameters -> {-1, > 1/10}]] > > At this point, you may have some alarming messages, but I believe it is > not really problematical... > > As you can control, it looks not bad : > > Plot[s[x], {x, -10, 20}, Epilog -> {Point /@ data}] > > Best regards > > Florian Jaccard > > > -----Message d'origine----- > De=A0: ratullochjk at gmail.com [mailto:ratullochjk at gmail.com] > Envoy=E9=A0: vendredi, 1. f=E9vrier 2008 08:20 > =C0=A0: mathgroup at smc.vnet.net > Objet=A0: [mg85198] Fourier Series Expansions and it's Coefficients = = > question revised tia > > Fourier Series Expansions and it's Coefficients question revised > > Greetings > > I've worked through a Fourier Series Expansion and it's Coefficients a= nd > have a better gasp at a how to explain my question. If I'm giving a > repeating wave at (T) period of 10 seconds with amplitudes > At 14, 18.7,9,4.1,6.7,6,6.3,8.4,4,2.9 how can I find the Fourier Serie= s > Expansions in Trigonometric form using mathematica 6. I've included a= n > example that I've worked through below > http://demos.onewithall.net/discrete_fourier_expansion_coefficients.jp= g > > I've been through mathematica site and they have examples of > Fourier Series but the examples they have are examples of equations th= ey > give you. I'm looking for an example where the equation isn't known a= nd > all you're given is the waveform, repeating period in seconds and the > amplitudes. Like in my example. > http://demos.onewithall.net/discrete_fourier_expansion_coefficients.jp= g > > Does an example exist? If not what are the steps needed in mathematica= 6 = > = > to > accomplish this. > > Tia simple > > > -- = DrMajorBob at bigfoot.com

**References**:**Fourier Series Expansions and it's Coefficients question revised tia***From:*ratullochjk@gmail.com