Dirichlet–Jordan test: Difference between revisions
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In [[mathematics]], the '''Dirichlet conditions''' are [[sufficient condition]] for a [[periodic function]] ''f''(''x''), to have a [[Fourier series]] representation or to possess a [[Fourier Transform]]. These conditions are named after [[Johann Peter Gustav Lejeune Dirichlet]]. |
In [[mathematics]], the '''Dirichlet conditions''' are [[sufficient condition]] for a [[periodic function]] ''f''(''x''), to have a [[Fourier series]] representation or to possess a [[Fourier Transform]]. These conditions are named after [[Johann Peter Gustav Lejeune Dirichlet]]. |
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Revision as of 02:36, 31 August 2007
In mathematics, the Dirichlet conditions are sufficient condition for a periodic function f(x), to have a Fourier series representation or to possess a Fourier Transform. These conditions are named after Johann Peter Gustav Lejeune Dirichlet.
The conditions are:
- f(x) must have a finite number of extrema in any given interval
- f(x) must have a finite number of discontinuities in any given interval
- f(x) must be absolutely integrable over a period.