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MathGroup Archive 2003

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Re: spectrum

  • To: mathgroup at smc.vnet.net
  • Subject: [mg39537] Re: [mg39532] spectrum
  • From: Sseziwa Mukasa <mukasa at jeol.com>
  • Date: Sat, 22 Feb 2003 03:37:36 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

On Friday, February 21, 2003, at 04:11 AM, thomas martinuzzo wrote:

>
> I'm a french student in a Engeenering school and I want to do spectrum 
> with
> mathematica.
> For exemple: How do to have the spectrum of
> x(t)= Sin[(2Pi/440)*t]
>

I assume you want a discretely sample spectrum.  The Fourier transform 
of Sin[(2Pi/440)*t] contains Delta functions, if you use UnitStep to 
eliminate nonzero values for t < 0 you can get an approximate 
continuous plot with

Plot[Evaluate[FourierTransform[Sin[2*Pi*t/400] UnitStep[t], t,
        w]], {w, -Pi/100, Pi/100}]

To get a discrete Fourier transform of length m and sample rate r use

ListPlot[Transpose[{Table[i/(
     m*r), {i, -Quotient[m, 2], Quotient[m, 2] - 1}], 
RotateRight[Re[Fourier[
           Table[Sin[2*Pi*i*r*m/400], {i, 0, m - 1}],
       FourierParameters -> {-1,
         1}]], Quotient[m, 2]]}], PlotJoined -> True, PlotRange -> All]

The first list is to provide the frequencies along the x axis.  Choose 
m and r appropriately.

Regards,

Ssezi



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