Dirichlet conditions

Dirichlet conditions guarantee that a periodic function can be exactly represented by its Fourier transform.

Readings edit

Conditions edit

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