The following is the graph of the periodic function (over the interval [-1,1]).

Below we see the approximations we get by taking one, two,... terms in the Fourier representation for (Click on the image to view the slow motion animation made of the displayed frames.)

Here is the graph of the periodic function (over the interval [-1,1]).

The approximations we get by taking one, two,... terms in the Fourier representation for are depicted below. Notice how fast the blue graphs (partial sums of Fourier series) approach the graph of the initial function.  (Click on the image to view the slow motion animation made of the displayed frames.)

Finally we take a look at the periodic function (over the interval [-1,1]).

Fourier approximations are in blue (as above)  (Click on the image to view the slow motion animation made of the displayed frames.)

© S.Kalajdzievski