Fourier-integral demo

The Fourier transform of a function $f:\mathbb{R}\to \mathbb{R}$ is defined by the formula \begin{equation*} \hat f(\omega) = \int_{-\infty}^\infty e^{-i 2\pi \omega t}f(t)\,d t, \end{equation*} (at least when $f$ is integrable). In the applet below one can draw the graph of a function (move the mouse from left to right and modify by moving again) which is suppoded to be $0$ outside the interval $[-5,5]$, and then the absolute value and argument or the real and imaginary parts of the Fourier transform are shown separately. Observe that the scale for the absolute value of the Fourier transform and of the function $f$ are not the same.

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