The general form of the Fourier Series is:-

The applet below shows some features of sines, cosines and rotating vectors.

Changing Fn changes what is shown.

Fn = 0 shows how counterrotating vectors can produce a cosine.

Fn = 1 shows how counterrotating vectors can produce a sine.

Fn = 2 shows how counterrotating vectors can produce a cosine with variable phase.

Fn = 3 shows how counterrotating vectors can produce a sine with variable phase.

Fn = 4 shows how a sine and a cosine can produce an anticlockwise rotating vector.

Fn = 5 shows how a sine and a cosine can produce a clockwise rotating vector.

Fn = 6 shows how a signal consisting of 2 sinusoids can be derived from rotating vectors. The frequency and phase of the second sinusoid can be set by r and f.

Fn = 7 shows how an approximate triangular signal can be represented by rotating vectors.

COPYRIGHT © 1996, 2010 Cuthbert Nyack.