Difference between revisions of "HW3.A David Record ECE301Fall2008mboutin" - Rhea

Revision as of 13:33, 16 September 2008

Time Invariant Systems

A system is time invariant if for any function x(t) a time shift of the function x(t-t0) the output function y(t) is time shifted in the same manner, y(t-t0).

A system is time variant if this time shift is not present, or is distorted in the output function.

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-== Invertible Systems ==
+== Time Invariant Systems ==
-A system is invertible if distinct inputs yield distinct outputs.
+A system is time invariant if for any function x(t) a time shift of the function x(t-t0) the output function y(t) is time shifted in the same manner, y(t-t0).
- Invertible System:
- y(t) = <math>\frac{3*x(t) + 8}{1}</math>
- x(t) = <math>\frac{y(t) - 8}{3}</math>
- x(t) -> |Sys 1| -> y(t) -> |Sys 2| -> x(t)
- The two equations are inverses of each other.
- Noninvertible System:
+A system is time variant if this time shift is not present, or is distorted in the output function.
- y(t) = <math>t^4</math>
- x(t) = <math>t</math>     ->     |Sys|     ->     y(t) = <math>t^4</math>
- x(t) = <math>-t</math>    ->     |Sys|     ->     y(t) = <math>t^4</math>
- The System is not invertible because for a given set of inputs you cannot differentiate which of the output will result.

Difference between revisions of "HW3.A David Record ECE301Fall2008mboutin" - Rhea

Revision as of 13:33, 16 September 2008

Time Invariant Systems

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