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8

Probably what you want is: ft[w_] = FourierTransform[UnitStep[t] Exp[-t], t, w] Otherwise, for t negative, the integral diverges. Also, you might want to check out the option FourierParameters. To plot: Plot[Abs[ft[w]], {w, 0, 10}]


5

Applying Fourier to a multi-dimensional array does a multi-dimensional FFT, so your first case generates the 2D FFT of all the trajectories. In your case you want to map the 1D FFT over each trajectory. ampFFT = Abs[Fourier[#,FourierParameters->{-1,1}]&/@(Transpose@x); Now each element of ampFFT is the 1D FFT of one trajectory, i.e. ampFFT[[i]] == ...


2

I think the problem your experience stems from trying to calculate the symbolic Fourier transform of Beam after numerical values have been substituted for xf and yf. This fails for $0$, as the variables disappear, and in general may not be accurate. Instead, pre-calculate the symbolic Fourier transform, then substitute in the numerical values of xf, yf, and ...



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