Discrete Systems and Digital Signal Processing with MATLAB

"Discrete linear systems and digital signal processing have been treated for years in separate publications. ElAli has skillfully combined these two subjects into a single and very useful volume. … Useful for electrical and computer engineering students and working professionals… a nice addition to the shelves of academic and public libraries. "Summing Up: Highly Recommended." — S.T. Karris, University of California, Berkeley in CHOICE Typically, books on linear systems combine coverage of both discrete and continuous systems all in a single volume. The result is usually a daunting mountain of information that fails to sufficiently explain either subject. With this in mind, Discrete Systems and Digital Signal Processing with MATLAB®, Second Edition responds to the need in engineering for a text that provides complete, focused coverage of discrete linear systems and associated problem solution methods. With its simplified presentation, this book follows a logical development that builds on basic mathematical principles to cover both discrete linear systems and signal processing. The author covers all traditional topics and includes numerous examples that are solved analytically and, when applicable, numerically using the latest version of MATLAB®. In addition to the classical coverage, the author includes complete and stand-alone chapters on IIR and FIR filter design, block diagrams, state-space, and sampling and transformations, as well as a unique chapter on FFT and its many applications. The book also introduces many examples using the MATLAB data acquisition toolbox in different chapters. Ideal either as a textbook for the required course in the electrical and computer engineering curriculum or as an updated refresher for seasoned engineers, this resource offers a wealth of examples, exercises, problems, and author insights.

Table of Contents:
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