Dirichlet conditions

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

[edit] 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.

[edit] Condition 2

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

[edit] Condition 3

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