Nonimaging optics - Revision history

en>Myasuda: /* Miñano design method using Poisson brackets */ sp

2014-12-25T19:41:50Z

Miñano design method using Poisson brackets: sp

← Older revision		Revision as of 21:41, 25 December 2014
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en>The Anome: *

2014-02-21T21:55:56Z

← Older revision		Revision as of 23:55, 21 February 2014
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	~~{{Unreferenced\|date=December 2006}}~~		Alyson is the tarot readings; [http://kard.dk/?p=24252 kard.dk], name people [http://netwk.hannam.ac.kr/xe/data_2/85669 cheap psychic readings] use to contact me and I believe it seems fairly good when you say it. One of the very best issues in the globe for him is performing ballet and he'll be beginning some thing else along with it. Credit authorising is how she makes a residing. North Carolina is the place he enjoys most but now he is contemplating other options.<br><br>Feel free to surf to my web page: free psychic readings - [http://www.edmposts.com/build-a-beautiful-organic-garden-using-these-ideas/ edmposts.com] -

	~~In [[signal processing]],~~ the ~~'''energy'''~~ ~~<math>E_s<~~/~~math> of a continuous-time signal ''x''(''t'') is defined as~~

	~~:<math>E_{s} \ \ = \ \ \langle x(t), x(t)\rangle \ \ = \int_{-\infty}^{\infty}{\|x(t)\|^2}dt<~~/~~math>~~

	~~Energy in this context is not, strictly speaking, the same as the conventional notion of [[energy]] in [[physics]] and the other sciences~~. ~~The two concepts are, however, closely related, and it is possible to convert from one to the other:~~
	~~:<math>E = {E_s \over Z}~~ = ~~{ 1 \over Z } \int_{-\infty}^{\infty}{\|x(t)\|^2}dt </math>~~
	~~:where ''Z'' represents the magnitude, in appropriate units of measure, of the load driven by the signal~~.

	~~For example, if ''x''(''t'') represents the [[electric potential\|potential]] (in [[volt]~~]~~s) of an electrical signal propagating across a transmission line~~, ~~then ''Z'' would represent the~~ [~~[characteristic impedance]] (in [[ohm]]s) of the transmission line. The units of measure for the signal energy <math>E_s<~~/~~math> would appear as volt<sup>2<~~/~~sup>·seconds, which is ''not'' dimensionally correct for energy in the sense of the physical sciences~~. ~~After dividing <math>E_s<~~/~~math> by ''Z'', however, the dimensions of ''E'' would become volt<sup>2<~~/~~sup>·seconds per ohm, which is equivalent to [[joule]]s, the [[SI]] unit for energy as defined in the physical sciences.~~

	~~==Spectral energy density==~~

	~~Similarly, the '''[[Spectral density\|spectral energy density]]''' of signal x(t) is~~

	~~:<math>\ E_s(f) = \|X(f)\|^2 <~~/~~math>~~
	~~where ''X''(''f'') is the [[Fourier transform~~]~~] of ''x''(''t'')~~.

	~~For example, if ''x''(''t'') represents the magnitude~~ of the ~~[[electric field]] component (~~in ~~[[volts]] per meter) of an optical signal propagating through [[free space]], then~~ the ~~dimensions of ''X''(''f'') would become volt·seconds per meter~~ and ~~<math>E_s(f)</math> would represent the signal~~'~~s spectral energy density (in volts<sup>2</sup>·second<sup>2</sup> per meter<sup>2</sup>) as~~ a ~~function of frequency ''f'' (in [[hertz]])~~. ~~Again, these units of measure are not dimensionally correct in~~ the ~~true sense of energy density as defined in physics~~. ~~Dividing~~ <~~math~~>~~E_s(f)~~<~~/math~~> ~~by ''Z''<sub>o</sub>, the characteristic impedance of~~ free ~~space (in ohms), the dimensions become joule~~-~~seconds per meter<sup>2<~~/~~sup> or, equivalently, joules per meter<sup>2<~~/~~sup> per hertz, which is dimensionally correct in [[SI]] units for spectral energy density~~.

	~~==Parseval's theorem==~~

	As a ~~consequence of [[Parseval's theorem]], one can prove that the signal energy is always equal to the summation across all frequency components of the signal's spectral energy density~~.

	~~==See also==~~
	* [[Signal processing]]
	* [[Parseval's theorem]]
	* [[Inner product]]

	~~[[Category:Signal processing]~~]

131.155.69.232: /* Theory */

2014-01-29T09:11:56Z

Theory

← Older revision		Revision as of 11:11, 29 January 2014
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	~~The person who wrote~~ the ~~post~~ is ~~called Jayson Hirano~~ and ~~he totally digs that title~~. The ~~preferred pastime for him~~ and ~~his kids~~ is ~~fashion and he~~'~~ll be beginning something else alongside with it~~. ~~Office supervising~~ is ~~my occupation~~. ~~Her family members lives~~ in ~~Ohio~~.<br><br>~~Also visit my blog post real psychic -~~ [~~http:~~//~~koreanyelp~~.~~com~~/~~index~~.~~php?document_srl~~=~~1798&mid~~=~~SchoolNews koreanyelp~~.~~com~~] -		{{Unreferenced\|date=December 2006}}

			In [[signal processing]], the '''energy''' <math>E_s</math> of a continuous-time signal ''x''(''t'') is defined as

			:<math>E_{s} \ \ = \ \ \langle x(t), x(t)\rangle \ \ = \int_{-\infty}^{\infty}{\|x(t)\|^2}dt</math>

			Energy in this context is not, strictly speaking, the same as the conventional notion of [[energy]] in [[physics]] and the other sciences. The two concepts are, however, closely related, and it is possible to convert from one to the other:
			:<math>E = {E_s \over Z} = { 1 \over Z } \int_{-\infty}^{\infty}{\|x(t)\|^2}dt </math>
			:where ''Z'' represents the magnitude, in appropriate units of measure, of the load driven by the signal.

			For example, if ''x''(''t'') represents the [[electric potential\|potential]] (in [[volt]]s) of an electrical signal propagating across a transmission line, then ''Z'' would represent the [[characteristic impedance]] (in [[ohm]]s) of the transmission line. The units of measure for the signal energy <math>E_s</math> would appear as volt<sup>2</sup>·seconds, which is ''not'' dimensionally correct for energy in the sense of the physical sciences. After dividing <math>E_s</math> by ''Z'', however, the dimensions of ''E'' would become volt<sup>2</sup>·seconds per ohm, which is equivalent to [[joule]]s, the [[SI]] unit for energy as defined in the physical sciences.

			==Spectral energy density==

			Similarly, the '''[[Spectral density\|spectral energy density]]''' of signal x(t) is

			:<math>\ E_s(f) = \|X(f)\|^2 </math>
			where ''X''(''f'') is the [[Fourier transform]] of ''x''(''t'').

			For example, if ''x''(''t'') represents the magnitude of the [[electric field]] component (in [[volts]] per meter) of an optical signal propagating through [[free space]], then the dimensions of ''X''(''f'') would become volt·seconds per meter and <math>E_s(f)</math> would represent the signal's spectral energy density (in volts<sup>2</sup>·second<sup>2</sup> per meter<sup>2</sup>) as a function of frequency ''f'' (in [[hertz]]). Again, these units of measure are not dimensionally correct in the true sense of energy density as defined in physics. Dividing <math>E_s(f)</math> by ''Z''<sub>o</sub>, the characteristic impedance of free space (in ohms), the dimensions become joule-seconds per meter<sup>2</sup> or, equivalently, joules per meter<sup>2</sup> per hertz, which is dimensionally correct in [[SI]] units for spectral energy density.

			==Parseval's theorem==

			As a consequence of [[Parseval's theorem]], one can prove that the signal energy is always equal to the summation across all frequency components of the signal's spectral energy density.

			==See also==
			* [[Signal processing]]
			* [[Parseval's theorem]]
			* [[Inner product]]

			[[Category:Signal processing]]

57.66.175.6: /* Compound parabolic concentrator */

2012-08-14T12:43:49Z

Compound parabolic concentrator

New page

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