Discrete Systems and Digital Signal Processing with MATLAB

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.

Signal Representation


Introduction


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


Convolution


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


Correlation


Some Insights






Fourier Series and the Fourier Transform of Discrete Signals


Introduction


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


Introduction


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


Introduction


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


Introduction


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


Introduction


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


Introduction


Design Process


IIR Filter Design Using MATLAB®


Some Insights






Finite Impulse Response Digital Filters


Introduction


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®


Some Insights





 


Bibliography





 


Index