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MathGroup Archive 1995

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Re: Fourier Question

  • To: mathgroup at christensen.cybernetics.net
  • To: mathgroup at christensen.cybernetics.net
  • Subject: [mg1628] Re: [mg1602] Fourier Question
  • From: el at qua.crl.melco.co.jp (E. Lange)
  • Date: Fri, 7 Jul 1995 00:43:05 -0400

> I have a question concerning the Mathematica command 'Fourier'
...
> 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]];

Just one minor problem here: in the phase factor Exp[I 2 Pi f0/N x],
x should be in the range {0, 127}:

b = 0;
f1=Table[N[g*Exp[I (x+63) b]],{x,-63,64}];
f2=Fourier[f1];

shift = 7;
b = shift 2Pi/128;
f1=Table[N[g*Exp[I (x+63) b]],{x,-63,64}];
f3=Fourier[f1];
f2 - RotateRight[f3, shift] // Chop

Eberhard Lange


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