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Continuous signals and systems with MATLAB
Chapter 1 Signal Representation 1.1 Examples of Continuous Signals 1.2 The Continuous Signal 1.3 Periodic and Nonperiodic Signals 1.4 General Form of Sinusoidal Signals 1.5 Energy and Power Signals 1.6 The Shifting Operation 1.7 The Reflection Operation 1.8 Even and Odd Functions 1.9 Time Scaling 1.10 The Unit Step Signal 1.11 The Signum Signal 1.12 The Ramp Signal 1.13 The Sampling Signal 1.14 The Impulse Signal 1.15 Some Insights: Signals in the Real World 1.16 End-of-Chapter Examples 1.17 End-of-Chapter Problems References Chapter 2 Continuous Systems 2.1 Definition of a System 2.2 Input and Output 2.3 Linear Continuous System 2.4 Time-Invariant System 2.5 Systems without Memory 2.6 Causal Systems 2.7 The Inverse of a System 2.8 Stable Systems 2.9 Convolution 2.10 Simple Block Diagrams 2.11 Graphical Convolution 2.12 Differential Equations and Physical Systems 2.13 Homogeneous Differential Equations and Their Solutions 2.14 Nonhomogeneous Differential Equations and Their Solutions 2.15 The Stability of Linear Continuous Systems: The Characteristic Equation 2.16 Block Diagram Representation of Linear Systems 2.17 From Block Diagrams to Differential Equations 2.18 From Differential Equations to Block Diagrams 2.19 The Impulse Response 2.20 Some Insights: Calculating y(t) 2.21 End-of-Chapter Examples 2.22 End-of-Chapter Problems References Chapter 3 Fourier Series 3.1 Review of Complex Numbers 3.2 Orthogonal Functions 3.3 Periodic Signals 3.4 Conditions for Writing a Signal as a Fourier Series Sum 3.5 Basis Functions 3.6 The Magnitude and the Phase Spectra 3.7 Fourier Series and the Sin-Cos Notation 3.8 Fourier Series Approximation and the Resulting Error 3.9 The Theorem of Parseval 3.10 Systems with Periodic Inputs 3.11 A Formula for Finding y(t) When x(t) Is Periodic: The Steady-State Response 3.12 Some Insight: Why the Fourier Series? 3.13 End-of-Chapter Examples 3.14 End-of-Chapter Problems References Chapter 4 The Fourier Transform and Linear Systems 4.1 Definition 4.2 Introduction 4.3 The Fourier Transform Pairs 4.4 Energy of Non-Periodic Signals 4.5 The Energy Spectral Density of a Linear System 4.6 Some Insights: Notes and a Useful Formula 4.7 End-of-Chapter Examples 4.8 End-of-Chapter Problems References Chapter 5 The Laplace Transform and Linear Systems 5.1 Definition 5.2 The Bilateral Laplace Transform 5.3 The Unilateral Laplace Transform 5.4 The Inverse Laplace Transform 5.5 Block Diagrams Using the Laplace Transform 5.6 Representation of Transfer Functions as Block Diagrams 5.7 Procedure for Drawing the Block Diagram from the Transfer Function 5.8 Solving LTI Systems Using the Laplace Transform 5.9 Solving Differential Equations Using the Laplace Transform 5.10 The Final Value Theorem 5.11 The Initial Value Theorem 5.12 Some Insights: Poles and Zeros 5.13 End-of-Chapter Examples 5.14 End-of-Chapter Problems References Chapter 6 State-Space and Linear Systems 6.1 Introduction 6.2 A Review of Matrix Algebra 6.3 General Representation of Systems in State-Space 6.4 General Solution of State-Space Equations Using the Laplace Transform 6.5 General Solution of the State-Space Equations in Real Time 6.6 Ways of Evaluating eAt 6.7 Some Insights: Poles and Stability 6.8 End-of-Chapter Examples 6.9 End-of-Chapter Problems References
Includes bibliographical references and index.
Dr. Taan S. ElAli, PhD, is a full professor of electrical engineering. He is currently the Chair of the Engineering Program and the ABET coordinator of the College of Aeronautics at ERAU-WW.