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

• To: mathgroup at smc.vnet.net
• Subject: [mg85293] RE: [mg85198] Fourier Series Expansions and it's Coefficients question revised tia
• From: "Jaccard Florian" <Florian.Jaccard at he-arc.ch>
• Date: Tue, 5 Feb 2008 06:10:24 -0500 (EST)
• References: <200802010720.CAA10016@smc.vnet.net>

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 and
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 Series
Expansions in Trigonometric form using mathematica 6.  I've included an
example that I've worked through below
http://demos.onewithall.net/discrete_fourier_expansion_coefficients.jpg

I've been through mathematica site and they have examples of
Fourier Series but the examples they have are examples of equations they
give you.  I'm looking for an example where the equation isn't known and
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.jpg

Does an example exist? If not what are the steps needed in mathematica 6 =
to
accomplish this.

Tia simple

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