Fourier Question

• To: mathgroup at christensen.cybernetics.net
• Subject: [mg1602] Fourier Question
• From: jt12799 at glibm3.cen.uiuc.edu (Jehan Tsai)
• Date: Tue, 4 Jul 1995 01:58:29 -0400
• Organization: University of Illinois at Urbana

```I have a question concerning the Mathematica command 'Fourier'
Recently, I have been experimenting with this command for a program I have
been working on that requires it.  For the most part, it seems to work as
expected, except when we multiply the list by Exp[I b x], which is supposed
to cause a shift in the frequency domain.  However, it does not seem to
perform as expected shifting the function around strangely in the frequency
domain.  According to references, Exp[I 2 Pi f0/N x] Should cause a shift
of f0, but does not.  Below are the commands I used in my trial.

g=UnitStep[x+5]-UnitStep[x-5];
b= ;
f1=Table[N[g*Exp[I x b]],{x,-63,64}];
f2=Fourier[f1];
ListPlot[Abs[f2]];

A comparison of this plot with the Fourier of sampled function g by itself
indicates that for whatever b I choose has no correlation on the shift itself.
I'm not sure what the problem is, whether I am misunderstanding the actual
code, the way Mathematica does the FFT or whether I am just plotting the
samples over an incorrect interval.  I am interested in any help or
suggestions in what the problem is.  Thanks in advance.

J.T. Tsai
------------------------------------------------------------------------------
J.T. Tsai    jt12799 at coewl.cen.uiuc.edu |  "Oh no we're in the hands of
University of Illinois-Urbana/Champaign	|           engineers!!!"
Dept. of Electrical Engineering     |  Dr. Ian Malcolm, >>Jurassic Park<<
------------------------------------------------------------------------------

```

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