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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. | ||
+ | |||
+ | 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
Contents
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 $)