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A system is called time invariance if and only if: | A system is called time invariance if and only if: | ||
| − | <math>x(t) --> [system] --> [time delay | + | <math>x(t) --> [system] --> [time delay] --> y(t)\,</math> |
| − | + | yields the same result as | |
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| − | <math> | + | <math>x(t) --> [time delay] --> [system] --> y(t) \,</math> |
| − | + | Remember: delay --> for only every function of t, change the t into t with the offset | |
| + | == Example of a time invariance system == | ||
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| − | <math> | + | <math>y(t) = x(t) \,</math> |
| − | <math> | + | <math>x(t) --> [system] --> x(t) --> [timedelay] --> x(t-1) \,</math> |
| − | + | ||
| − | + | ||
| − | + | ||
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| + | it yields the same result as: | ||
| + | <math>x(t) --> [timedelay] --> x(t-1) --> [system] --> x(t-1) \,</math> | ||
== Example of a non time invariance system == | == Example of a non time invariance system == | ||
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| − | <math> | + | <math>y(t) = t * x(t) \,</math> |
| − | <math> | + | <math>x(t) --> [system] --> t * x(t) --> [timedelay] --> t * x(t-1) \,</math> |
| − | + | it yields not the same result as: | |
| − | <math> | + | <math>x(t) --> [timedelay] --> x(t-1) --> [system] --> (t-1) x(t-1) \,</math> |
== Reference == | == Reference == | ||
Latest revision as of 18:15, 10 September 2008
Contents
Time Invariance
A system is called time invariance if and only if:
$ x(t) --> [system] --> [time delay] --> y(t)\, $
yields the same result as
$ x(t) --> [time delay] --> [system] --> y(t) \, $
Remember: delay --> for only every function of t, change the t into t with the offset
Example of a time invariance system
$ y(t) = x(t) \, $
$ x(t) --> [system] --> x(t) --> [timedelay] --> x(t-1) \, $
it yields the same result as:
$ x(t) --> [timedelay] --> x(t-1) --> [system] --> x(t-1) \, $
Example of a non time invariance system
$ y(t) = t * x(t) \, $
$ x(t) --> [system] --> t * x(t) --> [timedelay] --> t * x(t-1) \, $
it yields not the same result as:
$ x(t) --> [timedelay] --> x(t-1) --> [system] --> (t-1) x(t-1) \, $
Reference
http://kiwi.ecn.purdue.edu/ECE301Fall2008mboutin/index.php/Concepts_and_Formulae
