Applications of Fourier series

1. Signal analysis and filtering: a periodic signal (such as a square wave or a rectified waveform) is split into harmonics, so that the bandwidth needed and the effect of a filter or channel can be found. Harmonics beyond the system bandwidth are removed.
2. Circuit and power analysis: the response of linear circuits to non-sinusoidal periodic inputs (rectifiers, switching waveforms) is found by applying each harmonic separately and adding the results; it is also used for harmonic distortion in power systems.

Other uses include communication (modulation, spectrum analysers), heat conduction, vibration analysis and image/audio compression.