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# lecture6 - EE313 Linear Systems and Signals Fall 2010...

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EE313 Linear Systems and Signals Fall 2010 Initial conversion of content to PowerPoint by Dr. Wade C. Schwartzkopf Prof. Brian L. Evans Dept. of Electrical and Computer Engineering The University of Texas at Austin Discrete-Time Signals and Systems

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6 - 2 Signals A function, e.g. sin( t ) in continuous-time or sin(2 π n / 10) in discrete-time, useful in analysis A sequence of numbers, e.g. {1,2,3,2,1} which is a sampled triangle function, useful in simulation A collection of properties, e.g. even, causal, and stable, useful in reasoning about behavior A piecewise representation, e.g. A functional, e.g. δ ( t ) ( 29 < = = 0 for 0 0 for 2 1 0 for 1 t t t t u = otherwise 0 0 for 1 ] [ n n u
6 - 3 Kronecker Impulse (Function) Let δ [ n ] be a discrete-time impulse function, a.k.a. the Kronecker delta function: Impulse response h [ n ] : response of a discrete- time LTI system to a discrete impulse function [ ] = = 0 0 0 1 n n n δ n δ [ n ] 1

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6 - 4 ( 29 ( 29 { } t x T t y = { } ] [ ] [ n x T n y = T {•} y ( t ) x ( t ) T {•} y [
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