Transcription of 1 Z-Transforms, Their Inverses Transfer or System Functions
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1 Z-Transforms, Their Inverses Transfer or System Functions
1Z-Transforms, Their InversesTransfer or System FunctionsProfessor Andrew E. Yagle, EECS 206 Instructor, Fall 2005 Dept. of EECS, The University of Michigan, Ann Arbor, MI 48109-2122I. AbstractThe purpose of this document is to introduce EECS 206 students to the z- transform and what it s for. Italso introduces Transfer ( System ) Functions and shows how to use them to relate System Table of contents by sections:1. Abstract (you re reading this now)2. Forward Z-Transforms: How do I compute z-transforms?3. inverse Z-Transforms: How do I undo a z- transform ?4. Transfer ( System ) Functions : What are they for?5. Poles and Zeros: Transient and Frequency Responses6. The Atlanta Airport: (Has he completely lost his mind?)7. Half-Dozen Examples: This stuff is actually very useful!Why should you care about z-transforms and Transfer Functions ? Because of problems like this:Giventhat the response of an LTI System to input (12)nu[n] is output{0,0,1}= [n 2],Computethe response of the System to input 2 cos( 3n).
1 Z-Transforms, Their Inverses Transfer or System Functions Professor Andrew E. Yagle, EECS 206 Instructor, Fall 2005 Dept. of EECS, The University of Michigan, Ann Arbor, MI 48109-2122
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