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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Comments, questions!!!