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== Linear System == | == Linear System == | ||
| − | A system is linear if for any complex constants a and b and for any inputs <math>x_1(t) and x_2(t)</math> yielding output <math>y_1(t) and y_2(t)</math> respectively, the response is <math>a*x_1(t)+b*x_2(t) ==> [SYSTEM] ==> a*y_1(t) + b*y_2(t)</math> | + | A system is linear if for any complex constants a and b and for any inputs <math>x_1(t)</math> and <math>x_2(t)</math> yielding output <math>y_1(t)</math> and <math>y_2(t)</math> respectively, the response is <math>a*x_1(t)+b*x_2(t) ==> [SYSTEM] ==> a*y_1(t) + b*y_2(t)</math> |
| + | A system is nonlinear if for any complex constants a and b and for any inputs <math>x_1(t)</math> and <math>x_2(t)</math> yielding output <math>y_1(t)</math> and <math>y_2(t)</math> respectively, the response is <math>a*x_1(t)+b*x_2(t) ==> [SYSTEM] ==> z(t)</math> where <math> z(t) </math> is NOT the constants a and b multiplied by the outputs <math>y_1(t)</math> and <math>y_2(t)</math> | ||
| + | == Time Invariant System == | ||
| − | + | A system is called time invariant if for any input signal x(t) yielding output y(t) and for any time <math>t_0</math> the output to the shifted input <math>x(t-t_0)</math> is the shifted output <math> y(t-t_0)</math>. | |
| − | + | A system is not time invariant if shifting the input does not yield the same output shifted by the same amount. | |
| − | + | ==Stable System== | |
| − | + | A system is stable if bounded inputs yield bounded outputs. | |
| − | + | A system is not stable if bounded inputs yield unbounded outputs. | |
Latest revision as of 17:50, 17 September 2008
Contents
Memoryless System
A memoryless system is a system for which for any real number $ t_0 $, the output at $ t_0 $ depends only on that value of t.
A system with memory is a system whose output depends on the value $ t_0 $ as well as another value of t for any given $ t_0 $
Causal System
A system is causal if the output at any given time only depends on the input in present and past (not the future)
A system is not causal if the output at any given time depends on input in the future.
Linear System
A system is linear if for any complex constants a and b and for any inputs $ x_1(t) $ and $ x_2(t) $ yielding output $ y_1(t) $ and $ y_2(t) $ respectively, the response is $ a*x_1(t)+b*x_2(t) ==> [SYSTEM] ==> a*y_1(t) + b*y_2(t) $
A system is nonlinear if for any complex constants a and b and for any inputs $ x_1(t) $ and $ x_2(t) $ yielding output $ y_1(t) $ and $ y_2(t) $ respectively, the response is $ a*x_1(t)+b*x_2(t) ==> [SYSTEM] ==> z(t) $ where $ z(t) $ is NOT the constants a and b multiplied by the outputs $ y_1(t) $ and $ y_2(t) $
Time Invariant System
A system is called time invariant if for any input signal x(t) yielding output y(t) and for any time $ t_0 $ the output to the shifted input $ x(t-t_0) $ is the shifted output $ y(t-t_0) $.
A system is not time invariant if shifting the input does not yield the same output shifted by the same amount.
Stable System
A system is stable if bounded inputs yield bounded outputs.
A system is not stable if bounded inputs yield unbounded outputs.
