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

Latest revision as of 12:46, 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),
is commutative with the other effects of the system.

x(t)   ->   |Sys|   ->   |time delay by t0|   -> a(t)
  
x(t)   ->   |time delay by t0|   ->   |Sys|   -> a(t)
 
If this resulting function a(t) is the same for both cascades then the system is time invariant.</nowiki>

Time Variant Systems:

A system is time variant if the results of the cascaded systems are not the same.

@@ Line 1: / Line 1: @@
-== Invertible Systems ==
+== Time Invariant Systems ==
+----
-A system is invertible if distinct inputs yield distinct outputs.
- Invertible System:
-  y(t) = <math>\frac{3*x(t) + 8}{1}</math>
+  A system is time invariant if for any function x(t), a time shift of the function x(t-t0),
+ is commutative with the other effects of the system.
-  x(t) = <math>\frac{y(t) - 8}{3}</math>
+  x(t)   ->   |Sys|   ->   |time delay by t0|   -> a(t)
-  x(t) -> |Sys 1| -> y(t) -> |Sys 2| -> x(t)
+  x(t)   ->   |time delay by t0|   ->   |Sys|   -> a(t)
-  The two equations are inverses of each other.
+  If this resulting function a(t) is the same for both cascades then the system is time invariant.</nowiki>
- Noninvertible System:
+==  Time Variant Systems: ==
- 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.
+  A system is time variant if the results of the cascaded systems are not the same.

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

Latest revision as of 12:46, 16 September 2008

Time Invariant Systems

Time Variant Systems:

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