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?