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An invertible system is one in which there is a one-to-one correlation between inputs and outputs.
 
An invertible system is one in which there is a one-to-one correlation between inputs and outputs.
  
Example of an '''invertible''' system:
+
*Example of an '''invertible''' system:
 
<math>y(t) = x(t)</math>
 
<math>y(t) = x(t)</math>
  
Example of a '''non-invertible''' system:
+
*Example of a '''non-invertible''' system:
 
<math>y(t) = |x(t)|</math>
 
<math>y(t) = |x(t)|</math>
  
(both x(t) = -3 and x(t) = 3 yield the same result)
+
In the second example, both x(t) = -3 and x(t) = 3 yield the same result.
  
 
==[[Causality_OldKiwi]]==
 
==[[Causality_OldKiwi]]==

Revision as of 22:50, 17 June 2008

The six basic properties of Systems_OldKiwi

Memory_OldKiwi

A system with memory has outputs that depend on previous (or future) inputs.

Example of a system with memory: $ y(t) = x(t - \pi) $

Example of a system without memory: $ y(t) = x(t) $

Invertibility_OldKiwi

An invertible system is one in which there is a one-to-one correlation between inputs and outputs.

  • Example of an invertible system:

$ y(t) = x(t) $

  • Example of a non-invertible system:

$ y(t) = |x(t)| $

In the second example, both x(t) = -3 and x(t) = 3 yield the same result.

Causality_OldKiwi

Stability_OldKiwi

Time Invariance_OldKiwi

Linearity_OldKiwi

Alumni Liaison

Correspondence Chess Grandmaster and Purdue Alumni

Prof. Dan Fleetwood