Problem with Fourier

• To: mathgroup at smc.vnet.net
• Subject: [mg43948] Problem with Fourier
• From: Miroslav Kobas <miroslav.kobas at mat.ethz.ch>
• Date: Wed, 15 Oct 2003 04:59:24 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```Hello all

It seems to me that Mathematica 5.0 calculates somehow strange the
discrete Fourier transform of a list of data, or i do not really
understand the maths behind it.
I would expect that the discrete Fourier transform of a finite object
shows maxima in Fourier space at the integer reciprocal indices. But
this does not seem to be the case in the following very simple examples.
The first Table (data1) shows maxima in Fourier space at points 1 and
17, the second Table (data2) at points 3 and 20 and the third Table
(data3) at points 4 and 39. How is this possible, shouldn't the maxima
in Fourier space always be located at the first and last point.
According to this, the maxima in Fourier space can be shifted by
changing the resolution in direct space.

thanks for hints

miroslav kob
as

data1= Table[Sin[x], {x,0,0.5*¥ð,0.1}];
data2=Table[Sin[x], {x,0,10,0.5}];
data3=Table[Sin[x], {x,0,20,0.5}];

ListPlot[Abs[Fourier[data1]], PlotStyle -> PointSize[0.02],
AxesOrigin -> {1, 0}, PlotRange -> All];
ListPlot[Abs[Fourier[data2]], PlotStyle -> PointSize[0.02],
AxesOrigin -> {1, 0}, PlotRange -> All];
ListPlot[Abs[Fourier[data3]], PlotStyle -> PointSize[0.02],
AxesOrigin -> {1, 0}, PlotRange -> All];

```

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