96.39.169.65: Quarks and all* leptons are thought to be strings, not just electrons.

2013-11-06T15:00:25Z

Quarks and all* leptons are thought to be strings, not just electrons.

← Older revision		Revision as of 17:00, 6 November 2013
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	~~The author~~ is ~~called Wilber Pegues~~. ~~Distributing manufacturing has been his occupation for some time~~. ~~Alaska~~ is the ~~only location I've been residing in~~ but ~~now I'm considering other options~~. ~~She~~ is ~~really fond~~ of ~~caving but she doesn'~~t ~~have the time recently~~.<br><br>~~Here~~ is ~~my page :: spirit messages; [http:~~//~~www~~.~~prayerarmor~~.~~com~~/~~uncategorized/dont-know~~-which~~-kind-~~of~~-hobby-~~to-~~take~~-up-~~read~~-the-~~following-tips~~/ ~~click the next webpage~~],		{{Unreferenced\|date=December 2009}}
			In [[signal processing]], a '''quadrature filter''' <math>q(t)</math> is the [[analytic signal\|analytic representation]] of the [[impulse response]] <math>f(t)</math> of a real-valued filter:

			:<math>
			q(t) = f_{a}(t) = \left(\delta(t) + {i \over \pi t} \right) * f(t)
			</math>

			If the quadrature filter <math>q(t)</math> is applied to a signal <math>s(t)</math>, the result is

			:<math>
			h(t) = (q * s)(t) = \left(\delta(t) + {i \over \pi t} \right) * f(t) * s(t)
			</math>

			which implies that <math>h(t)</math> is the analytic representation of <math>(f * s)(t)</math>.

			Since <math>q</math> is an analytic signal, it is either zero or complex-valued. In practice, therefore, <math>q</math> is often implemented as two real-valued filters, which correspond to the real and imaginary parts of the filter, respectively.

			An ideal quadrature filter cannot have a finite [[support (mathematics)\|support]], but by choosing the function <math>f(t)</math> carefully, it is possible to design quadrature filters which are localized such that they can be approximated reasonably well by means of functions of finite [[support (mathematics)\|support]].

			==Applications==
			=== Estimation of analytic signal ===

			Notice that the computation of an ideal [[analytic signal]] for general signals cannot be made in practice since it involves convolutions with the function

			:<math>
			{1 \over \pi t}
			</math>

			which is difficult to approximate as a filter which is either causal or of finite [[support (mathematics)\|support]], or both. According to the above result, however, it is possible to obtain an analytic signal by convolving the signal <math>s(t)</math> with a quadrature filter <math>q(t)</math>. Given that <math>q(t)</math> is designed with some care, it can be approximated by means of a filter which can be implemented in practice. The resulting function <math>h(t)</math> is the analytic signal of <math>f * s</math> rather than of <math>s</math>. This implies that <math>f</math> should be chosen such that convolution by <math>f</math> affects the signal as little as possible. Typically, <math>f(t)</math> is a band-pass filter, removing low and high frequencies, but allowing frequencies within a range which includes the interesting components of the signal to pass.

			===Single frequency signals===
			For single frequency signals (in practice narrow bandwidth signals) with frequency <math> \omega </math> the ''magnitude'' of the response of a quadrature filter equals the signal's amplitude ''A'' times the frequency function of the filter at frequency <math> \omega </math>.

			:<math>
			h(t) = (s * q)(t) = \frac{1}{2\pi} \int_{-\infty}^{\infty} S(u) Q(u) e^{i u t} du =
			\frac{1}{2\pi} \int_{-\infty}^{\infty} A \pi [\delta(u + \omega) + \delta(u - \omega)]
			Q(u) e^{i u t} du =
			</math>

			:<math>
			= \frac{A}{2} \int_{0}^{\infty} \delta(u - \omega) Q(u) e^{i u t} du =
			\frac{A}{2} Q(\omega) e^{i \omega t}
			</math>

			:<math>
			\|h(t)\| = \frac{A}{2} \|Q(\omega)\|
			</math>

			This property can be useful when the signal ''s'' is a narrow-bandwidth signal of unknown frequency. By choosing a suitable frequency function ''Q'' of the filter, we may generate known functions of the unknown frequency <math> \omega </math> which then can be estimated.

			==See also==
			* [[Analytic signal]]
			* [[Hilbert transform]]

			{{DEFAULTSORT:Quadrature Filter}}
			[[Category:Signal processing]]

en>Davida98: There was a slight mis-leading piece of information

2012-08-28T16:41:05Z

There was a slight mis-leading piece of information

New page

The author is called Wilber Pegues. Distributing manufacturing has been his occupation for some time. Alaska is the only location I've been residing in but now I'm considering other options. She is really fond of caving but she doesn't have the time recently.<br><br>Here is my page :: spirit messages; [http://www.prayerarmor.com/uncategorized/dont-know-which-kind-of-hobby-to-take-up-read-the-following-tips/ click the next webpage],

String (physics) - Revision history

96.39.169.65: Quarks and all* leptons are thought to be strings, not just electrons.

en>Davida98: There was a slight mis-leading piece of information