A function   f(x)   is periodic with a period   T   if the domain of   f(x)   contains   x + T   whenever it contains x,   and if   f(x) = f(x + T).

Any periodic waveform can be expressed by Fourier series provided that (Dirichlet conditions):

(1) if the function is discontinuous there are a finite number of discontinuities in one period.

(2) it has a finite average value for the period T.

(3) it has a finite number of positive and negative maxima.