(→Invertible Systems) |
(→Invertible Systems) |
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A system is invertible if distinct inputs yield distinct outputs. | A system is invertible if distinct inputs yield distinct outputs. | ||
| − | Invertible System: | + | Invertible System: |
| − | y(t) = <math>\frac{3*x(t) + 8}{1}</math> | + | y(t) = <math>\frac{3*x(t) + 8}{1}</math> |
| − | x(t) = <math>\frac{y(t) - 8}{3}</math> | + | x(t) = <math>\frac{y(t) - 8}{3}</math> |
| − | x(t) -> |Sys 1| -> y(t) -> |Sys 2| -> x(t) | + | x(t) -> |Sys 1| -> y(t) -> |Sys 2| -> x(t) |
| − | The two equations are inverses of each other. | + | The two equations are inverses of each other. |
| − | Noninvertible System: | + | Noninvertible System: |
| − | + | 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> |
| + | |||
| + | 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. | ||
Revision as of 12:23, 16 September 2008
Invertible Systems
A system is invertible if distinct inputs yield distinct outputs.
Invertible System:
y(t) = $ \frac{3*x(t) + 8}{1} $
x(t) = $ \frac{y(t) - 8}{3} $
x(t) -> |Sys 1| -> y(t) -> |Sys 2| -> x(t)
The two equations are inverses of each other.
Noninvertible System:
y(t) = $ t^4 $ x(t) = $ t $ -> |Sys| -> y(t) = $ t^4 $ x(t) = $ -t $ -> |Sys| -> y(t) = $ t^4 $
The System is not invertible because for a given set of inputs you cannot differentiate which of the output will result.
