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The Z Transform - Lecture Notes - Seminar Slide Show By Alexander D. Poularikas.

6.1 Introduction

A. One-Sided Z-Transform

6.2 The Z-Transform and Discrete Functions

6.3 Properties of the Z-Transform Linearity ? Shifting Property ? Time Scaling ? Periodic Sequence ? Multiplication by n and nT ? Convolution ? Initial Value ? Final Value ? Multiplication by (nT)k ? Initial Value of f(nT) ? Final Value for f(nT) ? Complex Conjugate Signal ? Transform of Product ? Parseval?s Theorem ? Correlation ? Transforms with Parameters

6.4 Inverse Z-Transform Power Series Method ? Partial Fraction Expansion ? Inverse Transform by Integration ? Simple Poles ? Multiple Poles ? Simple Poles Not Factorable ? F(z) is Irrational Function of z

B. Two-Sided Z-Transform

6.5 The Z-Transform

6.6 Properties Linearity ? Shifting ? Scaling ? Time Reversal ? Multiplication by nT ? Convolution ? Correlation ? Multiplication by e?anT ? Frequency Translation ? Product ? Parseval?s Theorem ? Complex Conjugate Signal

6.7 Inverse Z-Transform Power Series Expansion ? Partial Fraction Expansion ? Integral Inversion Formula

C. Applications

6.8 Solutions of Difference Equations with Constant Coefficients

6.9 Analysis of Linear Discrete Systems - Transfer Function ? Stability ? Causality ? Frequency Characteristics ? Z-Transform and Discrete Fourier Transform (DFT)

6.10 Digital Filters - Infinite Impulse Response (IIR) Filters ? Finite Impulse Responses (FIR) Filters

6.11 Linear, Time-Invariant, Discrete-Time, Dynamical Systems

6.12 Z-Transform and Random Processes Power Spectral Densities ? Linear Discrete-Time Filters ? Optimum Linear Filtering

6.13 Relationship Between the Laplace and Z-Transform Alexander D. Poularikas University of Alabama in Huntsville

6.14 Relationship to the Fourier Transform

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