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| − | + | == Causality == | |
| − | - | + | ----- |
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| + | '''Definition:''' A system is causal if and only if the output y(t) at any given time depends on the input x(t) in present and/or past times; so <math>y(a)</math> depends on <math>x(t)</math> where <math>t\le a</math>. | ||
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| + | '''Side Note:''' All memoryless systems are causal. | ||
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| + | '''Examples:''' | ||
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| + | Causal System: <math>y(t)=\frac{5t}{2}u(t-3)</math> | ||
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| + | This system is causal because it has an output y(t) that depends on an input <math>x(t)=\frac{5t}{2}u(t-3)</math> where x(t) is zero for all values of <math>t\le 0</math>. | ||
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| + | Non-Causal System: <math>y(t)=\frac{e^{-2t}}{3}u(t+2)</math> | ||
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| + | This system is not causal because it has an output y(t) that depends on an input <math>x(t)=\frac{e^{-2t}}{3}u(t+2)</math> where x(t) is not zero for all values of <math>t\le 0</math>. The input depends on values of time considered to be in the future => u(t+2). | ||
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| + | -Tylor Thompson | ||
Latest revision as of 16:19, 1 July 2009
Causality
Definition: A system is causal if and only if the output y(t) at any given time depends on the input x(t) in present and/or past times; so $ y(a) $ depends on $ x(t) $ where $ t\le a $.
Side Note: All memoryless systems are causal.
Examples:
Causal System: $ y(t)=\frac{5t}{2}u(t-3) $
This system is causal because it has an output y(t) that depends on an input $ x(t)=\frac{5t}{2}u(t-3) $ where x(t) is zero for all values of $ t\le 0 $.
Non-Causal System: $ y(t)=\frac{e^{-2t}}{3}u(t+2) $
This system is not causal because it has an output y(t) that depends on an input $ x(t)=\frac{e^{-2t}}{3}u(t+2) $ where x(t) is not zero for all values of $ t\le 0 $. The input depends on values of time considered to be in the future => u(t+2).
-Tylor Thompson
