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A system is memoryless if for any <math>t\in \mathbb{R}</math> only on the input at <math>t_0,</math> | A system is memoryless if for any <math>t\in \mathbb{R}</math> only on the input at <math>t_0,</math> | ||
| − | Eg: | + | |
| + | Eg: | ||
| + | |||
<pre> Y(t) = X(t) + X(t-1){ memoryless} | <pre> Y(t) = X(t) + X(t-1){ memoryless} | ||
| − | Y(t) = X(t)+X(t-1) { with memory}.<pre> | + | Y(t) = X(t)+X(t-1) { with memory}.</pre> |
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Eg: | Eg: | ||
| − | <pre> Y(t) = 2x(t) + 3 | + | <pre> Y(t) = 2x(t) + 3.</pre> |
| + | |||
| + | '''Causalty''' | ||
| + | |||
| + | A system is called causal if output at any given time only depends on input in present and past(not future)ie; for any time <math>t_0,</math> | ||
| + | |||
| + | Y(<math>t_0,</math>) only depends on X(t) with t<<math>t_0,</math> | ||
| + | |||
| + | Y(t) = X(t+1) {non causal} | ||
| + | |||
| + | Y(t) = X(t-1){causal} | ||
Latest revision as of 07:57, 18 September 2008
Memory less system
A system is memoryless if for any $ t\in \mathbb{R} $ only on the input at $ t_0, $
Eg:
Y(t) = X(t) + X(t-1){ memoryless}
Y(t) = X(t)+X(t-1) { with memory}.
Invertible systems
A system is invertible if distinct inputs yield distinct outputs.
Eg:
Y(t) = 2x(t) + 3.
Causalty
A system is called causal if output at any given time only depends on input in present and past(not future)ie; for any time $ t_0, $
Y($ t_0, $) only depends on X(t) with t<$ t_0, $
Y(t) = X(t+1) {non causal}
Y(t) = X(t-1){causal}
