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MathGroup Archive 1998

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Fourier series with Mathematica. Help!

  • To: mathgroup at smc.vnet.net
  • Subject: [mg12779] Fourier series with Mathematica. Help!
  • From: Peter Neumann <peter at iei.tu-clausthal.de>
  • Date: Wed, 10 Jun 1998 03:04:39 -0400
  • Organization: Rechenzentrum der TU Clausthal
  • Sender: owner-wri-mathgroup at wolfram.com

I've got problems to calculate FourierTrigSeries from periodic functions
containing UnitStep-Expressions under Mathematica 3.0.  (I now I have
to load <<Calculus`DiracDelta` first.)

I attached an example file containung two examples. The first, a
rectangular function using UnitStep, causes no proplems. The second
example combining Sin and UnitStep fails to integrate. But the
integration could be done easily by hand.

Can anybody help me?

************ InputForm ******************

<<Calculus`FourierTransform`
<<Calculus`DiracDelta`

f1 = 	UnitStep[t-Pi/4] - UnitStep[t-3*Pi/4] 
	-UnitStep[t-5*Pi/4] + UnitStep[t-7*Pi/4];

Plot[f1,{t,0,2*Pi}]

FourierTrigSeries[f1, {t,0,2*Pi}, 5]


f2 = 	(1+3*Sin[t])*UnitStep[-1-3*Sin[t]] 
	+(-1+3*Sin[t])*UnitStep[-1+3*Sin[t]];

Plot[f2, {t,0,2*Pi}]

FourierTrigSeries[f2, {t,0,2*Pi}, 5]


************ End of Example *****************


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