en>Yobot: /* Introduction: Kakutani's solution to the classical Dirichlet problem */WP:CHECKWIKI error fixes using AWB (10093)

2014-05-05T13:09:54Z

Introduction: Kakutani's solution to the classical Dirichlet problem: WP:CHECKWIKI error fixes using AWB (10093)

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	In [[communications system]]s, a [[communication channel]] may change with time. '''Coherence time''' is the time duration over which the channel impulse response is considered to be not varying. Such channel variation is much more significant in [[wireless]] communications systems, due to [[Doppler effect]]s.

	~~==Simple model==~~
	~~In a simple model, a signal <math>x(t)</math> transmitted at time <math>t_1</math> will be received as~~
	~~:<math>y_{t_1}(t) = x(t-t_1)*h_{t_1}(t),</math>~~
	~~where <math>h_{t_1}(t)</math> is the channel impulse response (CIR) at time <math>t_1</math>. A signal transmitted at time <math>t_2</math> will be received as~~
	~~:<math>y_{t_2}(t) = x(t-t_2)*h_{t_2}(t).</math>~~
	~~Now, if <math>h_{t_1}(t) - h_{t_2}(t)</math> is relatively small, the channel may be considered constant within the interval <math>t_1</math> to <math>t_2</math>.~~

	~~Coherence~~ time (<~~math~~>~~T_c~~</~~math~~>) will ~~therefore~~ be given by		Medical transcription can be a good way to make money online as a full time career. Formal training is required, and this can be costly. Additionally, it is necessary to have good computer and transcription equipment that works reliably. A great deal of work is available for people who are able and willing [http://www.comoganhardinheiro101.com/tag/opcoes-binarias/ ganhe dinheiro na internet] to invest in training and good equipment. Pay is quite substantial. You can sell your wares on the Internet to make money. Certain sites will help you to do your selling. You can personalize the t-shirts for your client. You can advertise by putting fliers up around the neighborhood or by using Craigslist. <br><br><br>Several websites out there pay for people to do tasks that cannot be handled by a computer. It might be flagging inappropriate activity or finding the name of a business on a receipt. 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	:<~~math~~>~~T_c~~ = ~~t_2 - t_1~~.</~~math~~>

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	~~Using [[Clarke~~'s ~~model]~~], ~~from~~ the ~~maximum Doppler frequency~~ <~~math~~>~~f_d~~</~~math> we can obtain 50% coherence time <ref name="shankar2002">Shankar~~, ~~2002<~~/~~ref><ref name="rappaport2002">Rappaport, 2002<~~/~~ref>~~
	~~:<math>T_c = \sqrt{\frac{9}{16 \pi f_d^2}}<~~/~~math>~~
	~~Usually~~, ~~we use~~ the ~~following relation~~<~~ref name="rappaport2002"/~~>
	:<~~math~~>~~T_c = \sqrt{\frac{9}{16 \pi}} \frac{1}{f_d} \simeq \frac{0~~.~~423}{f_d}<~~/~~math>~~

	=~~=References==~~
	~~<references/>~~

	~~[[Category:Communication]]~~
	~~[[ar:زمن الاتساق]~~]

en>Citation bot 1 at 01:32, 12 March 2011

2011-03-12T01:32:36Z

New page

In [[communications system]]s, a [[communication channel]] may change with time. '''Coherence time''' is the time duration over which the channel impulse response is considered to be not varying. Such channel variation is much more significant in [[wireless]] communications systems, due to [[Doppler effect]]s.

==Simple model==
In a simple model, a signal <math>x(t)</math> transmitted at time <math>t_1</math> will be received as
:<math>y_{t_1}(t) = x(t-t_1)*h_{t_1}(t),</math>
where <math>h_{t_1}(t)</math> is the channel impulse response (CIR) at time <math>t_1</math>. A signal transmitted at time <math>t_2</math> will be received as
:<math>y_{t_2}(t) = x(t-t_2)*h_{t_2}(t).</math>
Now, if <math>h_{t_1}(t) - h_{t_2}(t)</math> is relatively small, the channel may be considered constant within the interval <math>t_1</math> to <math>t_2</math>.

Coherence time (<math>T_c</math>) will therefore be given by
:<math>T_c = t_2 - t_1.</math>

==Relation with Doppler frequency==
Using [[Clarke's model]], from the maximum Doppler frequency <math>f_d</math> we can obtain 50% coherence time <ref name="shankar2002">Shankar, 2002</ref><ref name="rappaport2002">Rappaport, 2002</ref>
:<math>T_c = \sqrt{\frac{9}{16 \pi f_d^2}}</math>
Usually, we use the following relation<ref name="rappaport2002"/>
:<math>T_c = \sqrt{\frac{9}{16 \pi}} \frac{1}{f_d} \simeq \frac{0.423}{f_d}</math>

==References==
<references/>

[[Category:Communication]]
[[ar:زمن الاتساق]]

Stochastic processes and boundary value problems - Revision history

en>Yobot: /* Introduction: Kakutani's solution to the classical Dirichlet problem */WP:CHECKWIKI error fixes using AWB (10093)

en>Citation bot 1 at 01:32, 12 March 2011