Dirichlet conditions
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Dirichlet conditions guarantee that a periodic function can be exactly represented by its Fourier transform.
Readings[edit | edit source]
Conditions[edit | edit source]
Condition 1[edit | edit source]
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 | edit source]
Given any finite period of time the number of local maxima and minima of within that period is finite.
Condition 3[edit | edit source]
Given any finite period of time there is a finite number of discontinuities in the function