Dirichlet conditions

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

Readings

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Conditions

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Condition 1

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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

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

Condition 3

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