Linear Time Invariant System: Difference between revisions

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===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.
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.


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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>.
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>

Revision as of 22:18, 6 January 2010

are eigenfunctions of any LTI system. The eigenvalues are .


LTI System
Input Output

</math>

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