Cover
Half Page
Series Page
Title Page
Copyright Page
Dedication Page
Contents
Preface
About the Author
Acknowledgment
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
1.15.1. The Step Signal
1.15.2. The Impulse Signal
1.15.3. The Sinusoidal Signal
1.15.4. The Ramp Signal
1.15.5. Other Signals
1.16. End-of-Chapter Examples
1.17. End-of-Chapter Problems
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
2.13.1. Case When the Roots Are All Distinct
2.13.2. Case When Two Roots Are Real and Equal
2.13.3. Case When Two Roots Are Complex
2.14. Nonhomogeneous Differential Equations and Their Solutions
2.14.1. How Do We Find the Particular Solution?
2.15. The Stability of Linear Continuous Systems: The Characteristic Equation
2.16. Block Diagram Representation of Linear Systems
2.16.1. Integrator
2.16.2. Adder
2.16.3. Subtractor
2.16.4. Multiplier
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)
2.20.1. How Can We Find These Eigenvalues?
2.20.2. Stability and Eigenvalues
2.21. End-of-Chapter Examples
2.22. End-of-Chapter Problems
Chapter 3: Fourier Series
3.1. Review of Complex Numbers
3.1.1. Definition
3.1.2. Addition
3.1.3. Subtraction
3.1.4. Multiplication
3.1.5. Division
3.1.6. From Rectangular to Polar
3.1.7. From Polar to Rectangular
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
3.12.1. No Exact Sinusoidal Representation for x(t)
3.12.2. The Frequency Components
3.13. End-of-Chapter Examples
3.14. End-of-Chapter Problems
Chapter 4: The Fourier Transform and Linear Systems
4.1. Definition
4.2. Introduction
4.3. The Fourier Transform Pairs
4.4. Energy of Nonperiodic 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
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
5.5.1. Parallel Systems
5.5.2. Series Systems
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
5.12.1. The Poles of the System
5.12.2. The Zeros of the System
5.12.3. The Stability of the System
5.13. End-of-Chapter Examples
5.14. End-of-Chapter Problems
Chapter 6: State-Space and Linear Systems
6.1. Introduction
6.2. A Review of Matrix Algebra
6.2.1. Definition, General Terms, and Notations
6.2.2. The Identity Matrix
6.2.3. Adding Two Matrices
6.2.4. Subtracting Two Matrices
6.2.5. Multiplying a Matrix by a Constant
6.2.6. Determinant of a 2 ร 2 Matrix
6.2.7. Transpose of a Matrix
6.2.8. Inverse of a Matrix
6.2.9. Matrix Multiplication
6.2.10. Diagonal Form of a Matrix
6.2.11. Exponent of a Matrix
6.2.12. A Special Matrix
6.2.13. Observation
6.2.14. Eigenvalues of a Matrix
6.2.15. Eigenvectors of a Matrix
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 e At
6.6.1. First Method: A Is a Diagonal Matrix
6.6.2. Second Method: A Is of the Form
6.6.3. Third Method: Numerical Evaluation, A of Any Form
6.6.4. Fourth Method: The CayleyโHamilton Approach
6.6.5. Fifth Method: The Inverse Laplace Method
6.6.6. Sixth Method: Using the General Form of ฮฆ(t) = e At and Its Properties
6.7. Some Insights: Poles and Stability
6.8. End-of-Chapter Examples
6.9. End-of-Chapter Problems
Index