Linear Time Invariant System: Difference between revisions

Revision as of 21:18, 6 January 2010

$===LinearTimeInvariantSystems(LTISystems)===Alineartimeinvariantsystemisonethatislinear(superpositionandproportionalityapply)andonethatdoesn'tchangewithtime.Forexampleacircuitwithfixedcapacitors,resistors,andinductorshavinganinputandanoutputislinearandtimeinvariant.Ifacapacitorchangedvaluewithtime,thenitwouldnotbetimeinvariant.===EigenfunctionsandEigenvaluesofanLTISystems===Itisaninterestingexercisetoshowthat<math>e^{j\omega t}$ are eigenfunctions of any LTI system. The eigenvalues are $\omega$ .

LTI System
Input	Output
$\delta (t)$	$h(t)$
$\delta (t=\lambda )$	$h(t-\lambda )$

</math>

@@ Line 1: / Line 1: @@
-===Linear Time Invariant Systems (LTI Systems)===
+<math>===Linear Time Invariant Systems (LTI Systems)===
 A linear time invariant system is one that is linear (superposition and proportionality apply) and one that doesn't change with time.  For example a circuit with fixed capacitors, resistors, and inductors having an input and an output is linear and time invariant.  If a capacitor changed value with time, then it would not be time invariant.
@@ Line 5: / Line 5: @@
 It is an interesting exercise to show that <math>e^{j\omega t}</math> are eigenfunctions of any LTI system.  The eigenvalues are <math>\omega</math>.
+{| class="wikitable" border="1"
+|+ LTI System
+! Input !! Output
+|-
+| <math>\delta (t)</math> || <math>h(t)</math>
+|-
+| <math>\delta (t= \lambda )</math> || <math>h(t-\lambda )</math>
+|}
+</math>

Linear Time Invariant System: Difference between revisions

Revision as of 21:18, 6 January 2010

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