Dirichlet conditions

Dirichlet conditions guarantee that a periodic function $$x(t)$$ can be exactly represented by its Fourier transform.

Readings

 * Dirichlet conditions

Condition 1
The function must be absolutely integrable over a single period $$T$$. This is equivalent to the statement that the area enclosed between the abcissa and the function is finite over a single period.

$$\int_T|x(t)|<\infty$$

Condition 2
Given any finite period of time the number of local maxima and minima of $$x(t)$$ within that period is finite.

Condition 3
Given any finite period of time there is a finite number of discontinuities in the function $$x(t)$$