SIGNALS & SYSTEMS
SIGNALS & SYSTEMS ECSE 2410
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This 1 page Class Notes was uploaded by Immanuel Brakus PhD on Monday October 19, 2015. The Class Notes belongs to ECSE 2410 at Rensselaer Polytechnic Institute taught by Staff in Fall. Since its upload, it has received 60 views. For similar materials see /class/224788/ecse-2410-rensselaer-polytechnic-institute in ELECTRICAL AND COMPUTER ENGINEERING at Rensselaer Polytechnic Institute.
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Date Created: 10/19/15
Outline 12 Topic 12 The z Transform ECSE 2410 Signals and Systems Fall 2003 Topic 12 The z Transform The De ning Sum Read 101 The Laplace Transform Study Video 161 Intro to zTransforms Study Video 162 zTransform of Impulses and Shifted Impulses Study Video 163 z Transform of a Periodic Sequence Study Video 164 zTransform of a Periodic Sequence using Superposition Don t worry too much about the ROC Be sure you understand poles and zeros The Inverse zTransform Read 103 The Inverse z Transform Read 106 Some zTransform Pairs Study Video 168 Inverse z Transforms Be sure you understand the partial fraction technique and how to use Table 102 especially for secondorder systems like pairs 912 Also know how to use the powerseries and long division techniques for inverse z Transforms as in Examples 1012 and 1013 Geometric Evaluation Read 104 Geometric Evaluation of the FT from the PoleZero Plot Don t worry too much about geometric evaluation of the phase Properties of the z Transform ea 105 Properties of the z Transform Study Video 165 Shifting Property in z Transforms Study Video 167 Veri cation of Delay Property Don t worry so much about what happens to the ROC Know how to use all of the properties in Table 101 Causality and Stability Read 107 Analysis of LTI Systems with the zTransform Read 1071 Causality Read 1072 Stability Read 1074 Examples Relating System Behavior to System Function Study Video 169 Step and Impulse Reponses ofa DT LTI System Key fact a causal stable discretetime system has all of its poles inside the unit circle Difference Equations Read 1073 LTI Systems Characterized by LCC DEs Read 109 The Unilateral zTransform Study Video 166 zTransform to solve a 1st order ODE Know when to use the unilateral zTransform and how to deal with initial conditions See also Study Videos in Topic 15 for more details on how to solve difference equations 1