Dirichlet Conditions - Revision history

Andrew: /* Condition 3. */

2006-10-04T06:01:10Z

Condition 3.

← Older revision		Revision as of 23:01, 3 October 2006
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	Over any period, <math> f(t) </math> can have only a finite number of discontinuities.		Over any period, <math> f(t) </math> can have only a finite number of discontinuities.


	<small> Information Referenced from <u>Linear Circuit Analysis <math> 2^{nd} </math> Edition</u> by DeCarlo & Lin		<small> Information Referenced from <u>Linear Circuit Analysis <math> 2^{nd} </math> Edition</u> by DeCarlo & Lin

Andrew: /* Condition 3. */

2006-10-04T06:00:20Z

Condition 3.

← Older revision		Revision as of 23:00, 3 October 2006
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	Over any period, <math> f(t) </math> can have only a finite number of discontinuities.		Over any period, <math> f(t) </math> can have only a finite number of discontinuities.

			<small> Information Referenced from <u>Linear Circuit Analysis <math> 2^{nd} </math> Edition</u> by DeCarlo & Lin

Andrew: /* Condition 1. */

2006-10-04T05:55:08Z

Condition 1.

← Older revision		Revision as of 22:55, 3 October 2006
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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.

Andrew: /* Condition 3. */

2006-10-04T05:53:22Z

Condition 3.

← Older revision		Revision as of 22:53, 3 October 2006
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	===Condition 3.===		===Condition 3.===

	Over any period, <math> f \,(t) </math> can have only a finite number of discontinuities.		Over any period, <math> f(t) </math> can have only a finite number of discontinuities.

Andrew: /* Condition 3. */

2006-10-04T05:53:12Z

Condition 3.

← Older revision		Revision as of 22:53, 3 October 2006
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	===Condition 3.===		===Condition 3.===

	Over any period, <math> f(t) </math> can have only a finite number of discontinuities.		Over any period, <math> f \,(t) </math> can have only a finite number of discontinuities.

Andrew at 05:52, 4 October 2006

2006-10-04T05:52:18Z

New page

==Dirichlet Conditions==

===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>

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.

===Condition 2.===

Over any period of the signal, there must be only a finite number of minima and maxima. in other words, functions like <math> \sin \left ( \frac{1}{t} \right ) </math> are excluded. These functions are known as bounded variations.

===Condition 3.===

Over any period, <math> f(t) </math> can have only a finite number of discontinuities.