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Fourier series decomposition of a periodic signal

Signal carré

1.27 = (4 / PI)
1.27 * (sin(x) + sin(3x) / 3 + sin(5x) / 5 + sin(7x) / 7 + sin(9x) / 9 + ...)

Triangle signal

1.27 = (4 / PI)
1.57 - 1.27 * (cos(x) + cos(3x) / 9 + cos(5x) / 25 + cos(7x) / 49 + cos(9x) / 81 + ...)

Sawtooth signal

sin(x) + sin(2x) / 2 + sin(3x) / 3 + sin(4x) / 4 + sin(5x) / 5 + sin(7x) / 7 + ...

parabolic signal

(Pi² / 3) - 4 * (cos(x) - cos(2x) / 4 + cos(3x) / 9 - cos(4x) / 16 + ...)

Hyperbolic Signal

- [(Pi² / 3) - 4 * (cos(x) - cos(2x) / 4 + cos(3x) / 9 - cos(4x) / 16 + ...)]