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== 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: | ||
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y(t) = <math>\frac{3*x(t) + 8}{1}</math> | y(t) = <math>\frac{3*x(t) + 8}{1}</math> | ||
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x(t) = <math>\frac{y(t) - 8}{3}</math> | x(t) = <math>\frac{y(t) - 8}{3}</math> | ||
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x(t) -> |Sys 1| -> y(t) -> |Sys 2| -> x(t) | x(t) -> |Sys 1| -> y(t) -> |Sys 2| -> x(t) | ||
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The two equations are inverses of each other. | The two equations are inverses of each other. | ||
Noninvertible System: | Noninvertible System: | ||
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y(t) = <math>t^4</math> | y(t) = <math>t^4</math> | ||
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x(t) = <math>t</math> -> |Sys| -> y(t) = <math>t^4</math> | x(t) = <math>t</math> -> |Sys| -> y(t) = <math>t^4</math> | ||
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x(t) = <math>-t</math> -> |Sys| -> y(t) = <math>t^4</math> | x(t) = <math>-t</math> -> |Sys| -> y(t) = <math>t^4</math> | ||
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The System is not invertible because for a given set of inputs you cannot differentiate which of the output will result. | The System is not invertible because for a given set of inputs you cannot differentiate which of the output will result. | ||
Revision as of 13:23, 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.
