en>Addbot: Bot: Migrating 1 interwiki links, now provided by Wikidata on d:q5358165

2013-03-14T15:23:58Z

Bot: Migrating 1 interwiki links, now provided by Wikidata on d:q5358165

← Older revision		Revision as of 17:23, 14 March 2013
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	~~Hello~~. ~~Allow me introduce~~ the ~~writer~~. ~~Her name~~ is ~~Emilia Shroyer but it~~'s ~~not~~ the ~~most female name out there~~. ~~South Dakota~~ is ~~exactly where me~~ and ~~my spouse reside~~ and ~~my family members loves it~~. ~~To gather badges is what her family and her appreciate~~. ~~Managing people is his profession~~.<br><br>~~Stop~~ by ~~my site:~~ [http://~~www~~.~~streaming~~.~~iwarrior.net~~/~~blog~~/~~258268 std testing at home~~]		In [[mathematics]] and [[engineering]], the '''S plane''' is the name for the [[complex plane]] on which [[Laplace transform]]s are graphed. It is a mathematical domain where, instead of viewing processes in the [[time domain]] modelled with time-based functions, they are viewed as equations in the [[frequency domain]]. It is used as a graphical analysis tool in engineering and physics.

			A real function (f) in time 't' is translated into the 's' plane by taking the [[integral]] of the function, multiplied by <math>e^{-st}</math> from <math>0</math> to <math>\infty</math>, where s is a [[complex number]].

			:<math>\int_{0}^\infty f(t) e^{-st}\,dt \; \| \; s \; \in \mathbb{C}</math>

			One way to understand what this equation is doing is to remember how [[Fourier analysis]] works. In [[Fourier analysis]], harmonic sine and cosine waves are multiplied into the signal, and the resultant integration provides indication of a signal present at that frequency (i.e. the signal's energy at a point in the frequency domain). The 's' transform does the same thing, but more generally. The e<sup>-st</sup> not only catches frequencies, but also the real e<sup>-t</sup> effects as well. 's' transforms therefore cater not only for frequency response, but decay effects as well. For instance, a [[damped sine wave]] can be modeled correctly using 's' transforms.

			's' transforms are commonly known as [[Laplace transform]]s. In the 's' plane, multiplying by s has the effect of differentiating in the corresponding real time domain. Dividing by s integrates.

			Analysing the [[complex number\|complex]] roots of an 's' plane equation and plotting them on an [[Argand diagram]], can reveal information about the frequency response and stability of a real time system.

			==See also==
			*[[Root locus]]
			*[[State space (controls)]]

			==External links==
			* [http://dspcan.homestead.com/files/Ztran/zlap.htm Illustration of how the s-plane maps to the z-plane]

			[[Category:Fourier analysis]]

			{{Mathanalysis-stub}}

en>R'n'B: Fix links to disambiguation page Polarization

2012-03-18T15:03:23Z

Fix links to disambiguation page Polarization

New page

Hello. Allow me introduce the writer. Her name is Emilia Shroyer but it's not the most female name out there. South Dakota is exactly where me and my spouse reside and my family members loves it. To gather badges is what her family and her appreciate. Managing people is his profession.<br><br>Stop by my site: [http://www.streaming.iwarrior.net/blog/258268 std testing at home]

Electron bubble - Revision history

en>Addbot: Bot: Migrating 1 interwiki links, now provided by Wikidata on d:q5358165

en>R'n'B: Fix links to disambiguation page Polarization