       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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