I have an input sine wave of:

f=60 Hz.

a[x_]= Sin[(2*\[Pi]*f) * x];

If I want to have an input, the same sine wave but in the frequency domain, how it can be possible?

On paper, I can do it, but try to implement it on Mathematica. I tried Fourier transform but not able to plot the frequency response.

  • 2
    $\begingroup$ Try: FourierTransform[Sin[(2*\[Pi]*f)*x], x, w] $\endgroup$ Jan 13, 2023 at 9:47
  • 1
    $\begingroup$ @DanielHuber Thanks! as, I mentioned in the question the Fourier transform works but I am not able to plot the frequency response in Mathematica of input sine wave. $\endgroup$
    – a019
    Jan 13, 2023 at 9:56

1 Answer 1


I am not able to plot the frequency response in Mathematica

Do you mean like this?

f = 60;
fInRadians = 2*π*f;
signal = Sin[fInRadians*t];
y = FourierTransform[signal, t, w, FourierParameters -> {1, -1}];
tab = Table[{k, y /. w -> k}, {k, -3 fInRadians, 3 fInRadians, fInRadians}]
tab = tab /. DiracDelta[0] -> 1
tab[[All, 2]] = Map[Sign[Im[#]] Abs[#] &, tab[[All, 2]]];
ListPlot[tab, PlotStyle -> AbsolutePointSize[5], 
 AxesLabel -> {"frequency (Hz)", "|F(Ω|"}, 
 PlotRange -> {All, {-6, 6}}, Filling -> Axis, FillingStyle -> Red]

Mathematica graphics


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