Re: Fourier coefficients

• To: mathgroup at smc.vnet.net
• Subject: [mg32947] Re: [mg32935] Fourier coefficients
• From: BobHanlon at aol.com
• Date: Thu, 21 Feb 2002 02:06:59 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```In a message dated 2/20/02 2:31:21 AM, phil at icu.strath.ac.uk writes:

>I am trying to do something really "simple".  I want to Plot the Fourier
>
>coefficients as vertical lines.  The line height should be proportional
>
>to the magnitude of its respective coefficient.  I just can't seem to
>get it though.  Any ideas?
>

Needs["Calculus`FourierTransform`"];
Needs["Graphics`Colors`"];

FourierTrigSeries[t, t, 5]

Sin[2*Pi*t]/Pi - Sin[4*Pi*t]/(2*Pi) + Sin[6*Pi*t]/(3*Pi) -

Sin[8*Pi*t]/(4*Pi) + Sin[10*Pi*t]/(5*Pi)

m=8;
coef = Table[FourierSinCoefficient[t, t, n], {n,m}]

{1/Pi, -(1/(2*Pi)), 1/(3*Pi), -(1/(4*Pi)), 1/(5*Pi),

-(1/(6*Pi)), 1/(7*Pi), -(1/(8*Pi))}

Plot[{1/(n*Pi),-1/(n*Pi), Sin[(2n-1)*Pi/2]/(n*Pi)},
{n,1,m},

PlotStyle->{
{Green,AbsoluteDashing[{2,5}]},
{Green,AbsoluteDashing[{2,5}]},
{Blue,AbsoluteDashing[{5,5,2,5}]}},

Frame -> True,
Epilog->{Red,
Table[
Line[{{n,0},{n,coef[[n]]}}],
{n,m}]}];

Bob Hanlon
Chantilly, VA  USA

```

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