# Fourier Series Various Waveforms.

Cuthbert Nyack
The Fourier Series for a few simple functions is illustrated by the applet below. Scrollbar 0 can be changed from 0 to 68 and changes the function. In all cases, the function is shown in red. the reconstruction in green and the error in yellow.

Scrollbar 29 can be used to find the error at any point within a period. All the functions have variable parameters shown by the yellow text and the expressions for an and/or bn also shown on the applet.

Fn = 1 is a square wave.
Fn = 2 is a wave whose shape can be changed by scrollbar 17.
Fn = 3, 4, 5 are special cases of Fn = 2.
Fn = 6 is a triangle wave.
Fn = 7 is a quadratic triangle wave.
Fn = 8 is a parabolic wave.
Fn = 9 is a cubic wave.
Fn = 10 is a ramp wave.
Fn = 11 is a quadratic ramp wave.
Fn = 12 is another ramp wave.
Fn = 13 is another quadratic ramp wave.
Fn = 14 is a triangle pulse.
Fn = 15 is a quadratic pulse.
Fn = 16 is a cubic pulse.
Fn = 17 is a square to triangle wave whose shape can be changed by scrollbar 16.
Fn = 18, 19 are special cases of Fn = 17.
Fn = 20 is a rectangular pulse whose width can be changed by scrollbar 24.
Fn = 21, 22 are special cases of Fn = 20.
Fn = 23 is a pulse whose shape can be changed by scrollbars 18 and 24.
Fn = 24, 25, 26 are special cases of Fn = 23.
Fn = 27 is a pulse whose shape can be changed by scrollbars 18 and 24.
Fn = 28, 29, 30 are special cases of Fn = 27.
Fn = 31 is a square to rectangular wave whose shape can be changed by scrollbar 2.
Fn = 32, 33 are special cases of Fn = 31.
Fn = 34 is a square to triangle wave whose shape can be changed by scrollbar 4.
Fn = 35, 36 are special cases of Fn = 34.
Fn = 37 is a ramp to square wave whose shape can be changed by scrollbar 4.
Fn = 38, 39 are special cases of Fn = 37.
Fn = 40 is a triangle to ramp wave whose shape can be changed by scrollbar 4.
Fn = 41, 42 are special cases of Fn = 40.
Fn = 43 is a pulse whose shape can be changed by scrollbars 2, 8 and 10.
Fn = 44 to 49 are special cases of Fn = 43.
Fn = 50 is a double pulse whose shape can be changed by scrollbars 2, 7, 10 and 11.
Fn = 51 to 54 are special cases of Fn = 50.
Fn = 55 is a wave whose shape can be changed by scrollbars 5, 12, 13 and 14.
Fn = 56 to 59 are special cases of Fn = 55.
Fn = 60 is a wave whose shape can be changed by scrollbars 3, 7, 10 and 11.
Fn = 61 to 62 are special cases of Fn = 60.
Fn = 63 is a pulse whose shape can be changed by scrollbars 3 and 5.
Fn = 64 to 65 are special cases of Fn = 63.
Fn = 66 is a 'scr' pulse whose shape can be changed by scrollbar 4.
Fn = 67 to 68 are special cases of Fn = 66.

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COPYRIGHT © 2010, 2012 Cuthbert Nyack.