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==[[Stability_OldKiwi]]==
 
==[[Stability_OldKiwi]]==
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There are many types of stability, for this course, we first consider [[BIBO_OldKiwi]] (Bounded Input Bounded Output) stability.
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A system is BIBO stable if, for all bounded inputs (<math>\exist B \epsilon \Re, x(t) < B</math>), the output is also bounded (<math>y(t) < \infty</math>)
  
 
==[[Time Invariance_OldKiwi]]==
 
==[[Time Invariance_OldKiwi]]==
  
 
==[[Linearity_OldKiwi]]==
 
==[[Linearity_OldKiwi]]==

Revision as of 23:00, 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

A causal system has outputs that only depend on current and/or previous inputs.

  • Example of a causal system:

$ y(t) = x(t) + x(t - 1) $

  • Example of a non-causal system:

$ y(t) = x(t) + x(t + 1) $

Stability_OldKiwi

There are many types of stability, for this course, we first consider BIBO_OldKiwi (Bounded Input Bounded Output) stability.

A system is BIBO stable if, for all bounded inputs ($ \exist B \epsilon \Re, x(t) < B $), the output is also bounded ($ y(t) < \infty $)

Time Invariance_OldKiwi

Linearity_OldKiwi

Alumni Liaison

EISL lab graduate

Mu Qiao