lecture 3

# lecture 3 - Lecture3:IntrotoSystems Definition Properties...

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Lecture 3: Intro to Systems Definition Properties Linear Time Invariance (LTI) Systems System Interconnection

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Definition of System Anything that act or react on one or more signals ( INPUTS ) to produce one or more signals ( OUTPUT ). H Inputs x(t) x[n] Output y(t) y[n] “H” represents OPERATIONS the system performs on the inputs to produce the output. CT System: ifthe Inputs/Outputs are CT signals. DT System: ifthe Inputs/Outputs are DT signals.
Problems in System Analysis Known Inputs MODELING System ?? Known Outputs Known Inputs PREDICTION/ANALYSIS (*) Known System Outputs ?? Known Inputs DESIGN (*) Choose System Desired Outputs Inputs ?? INVERSE PROBLEM Known System Known Outputs *Focus of this course.

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System Properties Linearity: Given a system H, an input x 1 (t) produces an output y 1 (t) and another input x 2 (t) generates an output y 2 (t): H y 1 (t) x 1 (t) H y 2 (t) x 2 (t) The system is known to be LINEAR if the following superposition condition holds: H a.y 1 (t) + b.y 2 (t) a.x 1 (t) + b.x 2 (t)
System Properties Linearity : This can be expressed as the following. H y i (t) x 1 (t) a a x 2 (t) a.x 1 (t) b.x 2 (t) a.x 1 (t) + b.x 2 (t) a H b H x 1 (t) x 2 (t) y 1 (t) y 2 (t) y o (t) a.y 1 (t) + b.y 2 (t) AND If y i (t) = y o (t) , the superposition holds and the system ‘H’ is linear.

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## This note was uploaded on 11/03/2009 for the course BMEN 305 taught by Professor Meissner during the Spring '07 term at Texas A&M.

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lecture 3 - Lecture3:IntrotoSystems Definition Properties...

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