Im basically messing around with discrete Fourier-Transformation and I cant figure out how to apply it. I know there exists a predefined command, but I want to learn the computation behind it and im trying to figure out the details.

I have a list of data:

data=Table[{i,Sin[2*Pi*i/100]+Sin[2*Pi*i/25] + RandomReal[{-1,1}] },{i,100}];

And I have a function F[k] of the variable k. Which is defined like this: F[k]=Sum[{i=1,100},Exp[-I*k*i]*x[i]] where x[i] is equal to data[[i,2]].

I need help to Plot the function F[k].

  • 1
    $\begingroup$ Read docs of Fourier, see details section for definition and properties and relations section, it contains the formula you are looking for $\endgroup$
    – I.M.
    Aug 7, 2023 at 11:52

1 Answer 1


You have a syntax error in Sum. The sum is written like:

data = Table[{i, 
    Sin[2*Pi*i/100] + Sin[2*Pi*i/25] + RandomReal[{-1, 1}]}, {i, 100}];
F[k_] := Sum[Exp[-I*k*i]*data[[i, 2]], {i, 1, 100}]

Now you can plot the real and imaginary part like:

Plot[Re@F[k], {k, 0, 2Pi}]
Plot[Im@F[k], {k, 0, 2Pi}]

enter image description here


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