Fourier Series Complex Form
The general form of the Fourier Series is:-
Using the substitutions below in the general form:-
Positive frequencies correspond to anticlockwise rotating vectors
and negative frequencies to clockwise rotating vectors. The
coefficients dn can be obtained from the equation:-
The applet below shows some features of sines, cosines and
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
Fn = 5 shows how a sine and a cosine can produce a clockwise
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.
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COPYRIGHT © 1996, 2010 Cuthbert Nyack.