lecture22

# lecture22 - 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 Difference Equations

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22 - 2 Linear Difference Equations Discrete-time LTI systems can sometimes be characterized by difference equations y [ n ] = (1/2) y [ n -1] + (1/8) y [ n -2] + x [ n ] Taking z -transform of difference equation gives description of system in z -domain Σ x [ n ] y [ n ] Unit Delay Unit Delay 1/2 1/8 + + + y [ n -1] y [ n -2]
22 - 3 Advances and Delays Sometimes differential equations will be presented as unit advances rather than delays y [ n +2] – 5 y [ n +1] + 6 y [ n ] = 3 x [ n +1] + 5 x [ n ] One can make a substitution that reindexes the equation so that it is in terms of delays Substitute n with n -2 to yield y [ n ] – 5 y [ n -1] + 6 y [ n -2] = 3 x [ n -1] + 5 x [ n -2] Before taking the z -transform, recognize that we work with time n 0 so u [ n ] is often implied y [ n -1] → y [ n -1] u [ n ] y [ n -1] u [ n -1]

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22 - 4 Example
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lecture22 - EE313 Linear Systems and Signals Fall 2010...

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