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===Casual System=== | ===Casual System=== | ||
'''Casual system''' is a system where the output <math>y(t)</math> at some specific instant <math>t_0</math> only depends on the input <math>x(t)</math> for value of <math>t</math> less than or equal to <math>t_0</math>. | '''Casual system''' is a system where the output <math>y(t)</math> at some specific instant <math>t_0</math> only depends on the input <math>x(t)</math> for value of <math>t</math> less than or equal to <math>t_0</math>. | ||
| + | |||
| + | ====Example==== | ||
| + | Memoryless system | ||
| + | :<math>y \left( t \right) = 1 + x \left( t \right) \cos \left( \omega t \right)</math> | ||
| + | |||
===Non-casual System=== | ===Non-casual System=== | ||
'''Non-casual system''' is a system that has some dependence on input values from the future (in addition to possible dependence on past or current input values). | '''Non-casual system''' is a system that has some dependence on input values from the future (in addition to possible dependence on past or current input values). | ||
| + | ====Example==== | ||
| + | :<math>y(t)=\int_{-\infty}^{\infty } \sin (t+\tau) x(\tau)\,d\tau</math> | ||
Latest revision as of 16:45, 19 September 2008
Contents
Causal & Non-casual Systems
Casual System
Casual system is a system where the output $ y(t) $ at some specific instant $ t_0 $ only depends on the input $ x(t) $ for value of $ t $ less than or equal to $ t_0 $.
Example
Memoryless system
- $ y \left( t \right) = 1 + x \left( t \right) \cos \left( \omega t \right) $
Non-casual System
Non-casual system is a system that has some dependence on input values from the future (in addition to possible dependence on past or current input values).
Example
- $ y(t)=\int_{-\infty}^{\infty } \sin (t+\tau) x(\tau)\,d\tau $
