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Discrete Systems and Digital Signal Processing with MATLAB, Second Edition


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Table of Contents

Signal Representation


Why Do We Discretize Continuous Systems?

Periodic and Nonperiodic Discrete Signals

Unit Step Discrete Signal

Impulse Discrete Signal

Ramp Discrete Signal

Real Exponential Discrete Signal

Sinusoidal Discrete Signal

Exponentially Modulated Sinusoidal Signal

Complex Periodic Discrete Signal

Shifting Operation

Representing a Discrete Signal Using Impulses

Reflection Operation

Time Scaling

Amplitude Scaling

Even and Odd Discrete Signal

Does a Discrete Signal Have a Time Constant?

Basic Operations on Discrete Signals

Energy and Power Discrete Signals

Bounded and Unbounded Discrete Signals

Some Insights: Signals in the Real World

Discrete System

Definition of a System

Input and Output

Linear Discrete Systems

Time Invariance and Discrete Signals

Systems with Memory

Causal Systems

Inverse of a System

Stable System


Difference Equations of Physical Systems

Homogeneous Difference Equation and Its Solution

Nonhomogeneous Difference Equations and Their Solutions

Stability of Linear Discrete Systems: The Characteristic Equation

Block Diagram Representation of Linear Discrete Systems

From the Block Diagram to the Difference Equation

From the Difference Equation to the Block Diagram: A Formal Procedure

Impulse Response


Some Insights

Fourier Series and the Fourier Transform of Discrete Signals


Review of Complex Numbers

Fourier Series of Discrete Periodic Signals

Discrete System with Periodic Inputs: The Steady-State Response

Frequency Response of Discrete Systems

Fourier Transform of Discrete Signals

Convergence Conditions

Properties of the Fourier Transform of Discrete Signals

Parseval's Relation and Energy Calculations

Numerical Evaluation of the Fourier Transform of Discrete Signals

Some Insights: Why Is This Fourier Transform?

z-Transform and Discrete Systems


Bilateral z-Transform

Unilateral z-Transform

Convergence Considerations

Inverse z-Transform

Properties of the z-Transform

Representation of Transfer Functions as Block Diagrams

x(n), h(n), y(n), and the z-Transform

Solving Difference Equation Using the z-Transform

Convergence Revisited

Final-Value Theorem

Initial-Value Theorem

Some Insights: Poles and Zeroes

State-Space and Discrete Systems


Review on Matrix Algebra

General Representation of Systems in State Space

Solution of the State-Space Equations in the z-Domain

General Solution of the State Equation in Real Time

Properties of An and Its Evaluation

Transformations for State-Space Representations

Some Insights: Poles and Stability

Block Diagrams and Review of Discrete System Representations


Basic Block Diagram Components

Block Diagrams as Interconnected Subsystems

Controllable Canonical Form Block Diagrams with Basic Blocks

Observable Canonical Form Block Diagrams with Basic Blocks

Diagonal Form Block Diagrams with Basic Blocks

Parallel Block Diagrams with Subsystems

Series Block Diagrams with Subsystems

Block Diagram Reduction Rules

Discrete Fourier Transform and Discrete Systems


Discrete Fourier Transform and the Finite-Duration Discrete Signals

Properties of the DFT

Relation the DFT Has with the Fourier Transform of Discrete Signals, the z-Transform, and the Continuous Fourier Transform

Numerical Computation of the DFT

Fast Fourier Transform: A Faster Way of Computing the DFT

Applications of the DFT

Some Insights

Sampling and Transformations

Need for Converting a Continuous Signal to a Discrete Signal

From the Continuous Signal to Its Binary Code Representation

From the Binary Code to the Continuous Signal

Sampling Operation

How Do We Discretize the Derivative Operation?

Discretization of the State-Space Representation

Bilinear Transformation and the Relationship between the Laplace-Domain and the z-Domain Representations

Other Transformation Methods

Some Insights

Infinite Impulse Response Filter Design


Design Process

IIR Filter Design Using MATLAB (R)

Some Insights

Finite Impulse Response Digital Filters


FIR Filter Design

Design Based on the Fourier Series: The Windowing Method

From IIR to FIR Digital Filters: An Approximation

Frequency Sampling and FIR Filter Design

FIR Digital Design Using MATLAB (R)

Some Insights



About the Author

Taan S. ElAli, Ph.D, has been a full professor of electrical engineering since 2002. Earning the rare honor of senior membership in the IEEE, he has worked full time for about 17 years at several academic institutions nationally and internationally in the areas of curriculum development, accreditation, teaching, research, and leadership. A former Fulbright scholar, Dr. ElAli obtained his BS in electrical engineering in 1987 from The Ohio State University, Columbus, United States, and his MS in systems engineering in 1989 from Wright State University, Dayton, Ohio, United States. He earned another MS in applied mathematics and a Ph.D in electrical engineering--with a specialization in systems, controls, and signal processing--from the University of Dayton in 1991 and 1993, respectively. Among his many awards and accomplishments, Dr. ElAli has discovered a new approach to dynamic system identification. His extensive research and interest in revolutionizing the engineering education has led to the publishing of his Innovations in Engineering Education book.

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