Def:          Fourier series for periodic

where period of g(x) is periodic with period .

Note:       Since and , the Fourier series for periodic g(x) may also be written as

Def:          Fundamental frequency of periodic .

Ex:           

This sawtooth waveform has period . Therefore, the fundamental frequency is . Thus,

Ex:           

The above quadratic function is not periodic. It has no Fourier series representation, (unless we extract a section from it and make side-by-side copies so it becomes periodic). We might try to use a Fourier transform representation of g(x), but this approach would also fail, as the energy in the function is infinite: