Continuous Signals and Systems with MATLAB (Electrical Engineering Textbook Series)

Designed for a one-semester undergraduate course in continuous linear systems, Continuous Signals and Systems with MATLAB®, Second Edition presents the tools required to design, analyze, and simulate dynamic systems. It thoroughly describes the process of the linearization of nonlinear systems, using MATLAB® to solve most examples and problems. With updates and revisions throughout, this edition focuses more on state-space methods, block diagrams, and complete analog filter design.

New to the Second Edition

• A chapter on block diagrams that covers various classical and state-space configurations

• A completely revised chapter that uses MATLAB to illustrate how to design, simulate, and implement analog filters

• Numerous new examples from a variety of engineering disciplines, with an emphasis on electrical and electromechanical engineering problems

Explaining the subject matter through easy-to-follow mathematical development as well as abundant examples and problems, the text covers signals, types of systems, convolution, differential equations,Fourier series and transform, the Laplace transform, state-space representations, block diagrams, system linearization, and analog filter design. Requiring no prior fluency with MATLAB, it enables students to master both the concepts of continuous linear systems and the use of MATLAB to solve problems.

Preface
Signal Representation
Examples of Continuous Signals
The Continuous Signal
Periodic and Nonperiodic Signals
General Form of Sinusoidal Signals
Energy and Power Signals
The Shifting Operation
The Reflection Operation
Even and Odd Functions
Time Scaling
The Unit Step Signal
The Signum Signal
The Ramp Signal
The Sampling Signal
The Impulse Signal
Some Insights: Signals in the Real World
Continuous Systems
Definition of a System
Input and Output
Linear Continuous System
Time-Invariant System
Systems without Memory
Causal Systems
The Inverse of a System
Stable Systems
Convolution
Simple Block Diagrams
Graphical Convolution
Differential Equations and Physical Systems
Homogeneous Differential Equations and Their Solutions
Nonhomogeneous Differential Equations and Their Solutions
The Stability of Linear Continuous Systems:
The Characteristic Equation
Block Diagram Representation of Linear Systems
From Block Diagrams to Differential Equations
From Differential Equations to Block Diagrams
The Impulse Response
Some Insights: Calculating y( t)
Fourier Series
Review of Complex Numbers
Orthogonal Functions
Periodic Signals
Conditions for Writing a Signal as a Fourier Series Sum
Basis Functions
The Magnitude and the Phase Spectra
Fourier Series and the Sin-Cos Notation
Fourier Series Approximation and the Resulting Error
The Theorem of Parseval
Systems with Periodic Inputs
A Formula for Finding y( t) When x( t) Is Periodic: The Steady-State Response
Some Insight: Why the Fourier Series?
The Fourier Transform and Linear Systems
Definition
Introduction
The Fourier Transform Pairs
Energy of Nonperiodic Signals
The Energy Spectral Density of a Linear System
Some Insights: Notes and a Useful Formula
The Laplace Transform and Linear Systems
Definition
The Bilateral Laplace Transform
The Unilateral Laplace Transform
The Inverse Laplace Transform
Block Diagrams Using the Laplace Transform
Representation of Transfer Functions as Block Diagrams
Procedure for Drawing the Block Diagram from the Transfer Function
Solving LTI Systems Using the Laplace Transform
Solving Differential Equations Using the Laplace Transform
The Final Value Theorem
The Initial Value Theorem
Some Insights: Poles and Zeros
State-Space and Linear Systems
Introduction
A Review of Matrix Algebra
General Representation of Systems in State Space
General Solution of State-Space Equations Using the Laplace Transform
General Solution of the State-Space Equations in Real Time
Ways of Evaluating eAt
Some Insights: Poles and Stability
Block Diagrams
Introduction
Basic Block Diagram Components
Block Diagrams as Interconnected Subsystems
The Controllable Canonical Form Block Diagrams with Basic Blocks
The Observable Canonical Form Block Diagrams with Basic Blocks
The Diagonal Form Block Diagrams with Basic Blocks
The Parallel Block Diagrams with Subsystems
The Series Block Diagrams with Subsystems
Block Diagram Reduction Rules
Analog Filter Design
Introduction
Analogue Filter Specifications
Butterworth Filter Approximation
Chebyshev Filters
Elliptic Filter Approximation
Bessel Filters
Analog Frequency Transformation
Analog Filter Design Using MATLAB
How Do We Find the Cutoff Frequency Analytically?
Limitations
Comparison between Analog Filter Types
Implementation of Analog Filters
Some Insights: Filters with High Gain versus Filters with Low Gain and the Relation between the Time Constant and the Cutoff Frequency for First-Order Circuits and the Series RLC Circuit
Introduction to Nonlinear Systems
Introduction
Linear and Nonlinear Differential Equations
The Process of Linearization
Some Insights: The Meaning of Linear and Nonlinear
Index
Each chapter contains Examples, Problems, and References at the end.