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FourierTrigSeries[] and user-defined function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg96628] FourierTrigSeries[] and user-defined function
  • From: sagrailo at gmail.com
  • Date: Tue, 17 Feb 2009 06:32:53 -0500 (EST)

Am trying to have Mathematica to generated coefficient of Fourier
trigonometric series for simple step function, defined as follows:
  f[x_ /; Mod[x, 2*Pi] <= Pi] := 1
  f[x_ /; Mod[x, 2*Pi] > Pi] := 2

I'm able to get the plot of the function:
  Plot[f[x], {x, 0, 2*Pi}, PlotRange -> {0, 3}]

However, when I try to generate Fourier coefficients:
  FourierTrigSeries[f[x], x, 10]
Mathematica is just repeating the above expression as output (and
passing the expression to N[] or Evaluate[] doesn't help.

Any suggestion here?  Also, is it possible to not use Mod[] in the
function definition above, and to have Mathematica to "know" that it
should "extend" given function so that it behaves as periodic
function?

Thanks.


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