Dirichlet conditions

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

ReadingsEdit

ConditionsEdit

Condition 1Edit

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 2Edit

Given any finite period of time the number of local maxima and minima of   within that period is finite.

Condition 3Edit

Given any finite period of time there is a finite number of discontinuities in the function