Fourier-series demo
The Fourier coefficients of a periodic function with period $1$,
(or of a function defined on e.g. the interval $[0,1)$ and which is
the extended periodically) are given by the formula
\begin{equation*}
\hat f(n) = \int_0^1 e^{-i 2\pi n} f(t)\,dt.
\end{equation*}
In the applet below one can draw the graph of a periodic function
(move the mouse from left to right and
modify by moving again) and then the absolute value and argument or
the real an imaginary parts are shown separately. Observe that the
scales for the Fourier coefficients and for the function $f$ are not
the same.
The graph of the sum
\begin{equation*}
\sum_{n=-M}^M e^{i 2\pi t n}\hat f(n),
\end{equation*}
is drawn in blue.
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Comments, questions!!!