EE3TP4_5_SystemProperties_Lecture 6

# EE3TP4_5_SystemProperties_Lecture 6 - 1.5 Basic System...

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1.5 Basic System Properties There are some fundamental properties that many systems share regardless if they are C-T or D-T and regardless if they are electrical, mechanical, etc. The three main fundamental properties we will consider are: Causality Linearity Time-Invariance These overheads were originally developed by Mark Fowler at Binghamton University, State University of New York.

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Causality : A causal (or non-anticipatory) system’s output at a time t 1 does not depend on values of the input x ( t ) for t > t 1 The “future input” cannot impact the “current output” Systems in nature are causal! (?) A Causal system (with zero initial conditions) cannot have a non-zero output until a non-zero input is applied. But… we need to understand non-causal systems because theory shows that sometimes the “best” systems are non-causal! So we need to find causal systems that are as close to the best non-causal systems! t t Input Output Causal System t t Input Output Non-Causal System
: A system is linear if superposition always holds: Linear System x 1 ( t ) y 1 ( t ) Linear System x 2 ( t ) y 2 ( t ) Linear System x ( t ) = a 1 x 1 ( t ) + a 2 x 2 ( t ) y ( t ) = a 1 y 1 ( t ) + a 2 y 2 ( t ) Non-Linear x 1 ( t ) y 1 ( t ) Non-Linear x 2 ( t ) y 2 ( t ) Non-Linear x ( t ) = a 1 x 1 ( t ) + a 2 x 2 ( t ) y ( t ) a 1 y 1 ( t ) + a 2 y 2 ( t ) a 1 a 2 are constants. If this happens for a single example, it proves the non-linearity! This must be true for

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EE3TP4_5_SystemProperties_Lecture 6 - 1.5 Basic System...

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