Dirichlet conditions
From Wikiversity
Dirichlet conditions guarantee that a periodic function
can be exactly represented by its Fourier transform.
Condition 1 [edit]
The function must be absolutely integrable over a single period
. This is equivalent to the statement that the area enclosed between the abcissa and the function is finite over a single period.

Condition 2 [edit]
Given any finite period of time the number of local maxima and minima of
within that period is finite.
Condition 3 [edit]
Given any finite period of time there is a finite number of discontinuities in the function 