# Plotting an Almost Fourier Transform like 3Blue1Brown

Two years ago 3Blue1Brown posted this video. The important part starts at 9:38 to 9:54.

I am trying to plot his functions in Mathemtica. So, for the first plot with 2Hz I got

Plot[Sin[2*Pi*2*t] ,{t,0,2}]


which works perfectly fine. But I am not able to plot the "Almost Fourier = AF" Transform of that function. I think the definition of his AF is $$\mathfrak{F}_T\{f(t)\}(s)=\int\limits_{-T}^{T}f(t)e^{-2\pi its}\,\mathrm{d}t,$$ where $$T$$ is an arbitrary real number. For $$T\to\infty$$ we get the normal Fourier Transform, which is not practical to work with. I don't know what value he picked for $$T$$ but let's choose $$T=10$$. So, how can I program a plottable AF that looks exactly like the plot in his video?

g[s_] = -Integrate[(Sin[2*Pi*2*t] + Sin[2*Pi*4*t])*Exp[-2*Pi*I*t*s], {t, -tt, tt}];