Dirichlet Conditions: Difference between revisions

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===Condition 1.===
===Condition 1.===


Over any period <math> [t, t + T],\,f(t)</math> must have the property: <math> \int_t^{t+T} \mid f(t)\mid dt < \infty </math>
Over any period <math> [t, t + T],\,f(t)</math> must have the property: <math> \int_t^{t+T} \vert f(t)\vert \, dt < \infty </math>


In other words, <math> f(t) </math> is abosolutely integrable. The result of this property is that each of the Fourier coefficients <math> c_n </math> is finite.
In other words, <math> f(t) </math> is abosolutely integrable. The result of this property is that each of the Fourier coefficients <math> c_n </math> is finite.

Revision as of 22:55, 3 October 2006

Dirichlet Conditions

Condition 1.

Over any period must have the property:

In other words, is abosolutely integrable. The result of this property is that each of the Fourier coefficients is finite.

Condition 2.

Over any period of the signal, there must be only a finite number of minima and maxima. in other words, functions like are excluded. These functions are known as bounded variations.

Condition 3.

Over any period, can have only a finite number of discontinuities.