TABLE OF CONTENTS
CHAPTER 1.....Introduction to Signals and Systems
- Philosophy
- What is a Signal?
- What is a System?
CHAPTER 2.....Continuous-Time Systems
- A Differential Equation is a System
- Finding the Solution
- Integrator-Adder-Gain Block Diagrams
- State Equations
CHAPTER 3.....The Frequency Domain
- Why a New Domain?
- Complex Frequency
- Eigenfunctions
- An Example Problem
- Impedance
- Steady State Analysis
CHAPTER 4.....The Laplace Transform
- What is the Laplace Transform?
- Unilateral vs. Bilateral
- Region of Convergence
- Bilateral Laplace Transform Properties
- Table of Transform Pairs
- The Inverse Laplace Transform
- Initial and Final Value Theorems
CHAPTER 5.....CT Systems Analysis
- The System Function
- Poles and Zeros
- Converting Differential Equations to System Functions
- Zero Input Response
- Zero State Response
- The Impulse Response
- Combining Systems
CHAPTER 6.....Bode Plots
- What is a Bode Plot?
- Calculating the Frequency Response
- The Asymptotic Approximations
- Relationship to the Pole/Zero plot
- Dealing with Multiple Poles and Zeros
- Summary of Bode Plotting Rules
- Dealing with Complex Poles/Zeros
- Sample Bode Plot Questions
- Calculating the Frequency Response Experimentally
CHAPTER 7.....Discrete Signals and Z-Transforms
- A New Type of Signal
- The Z-Transform
- Region of Convergence (ROC)
- Z-Transform Pairs
- Z-Transform Properties
- Inverse Z-Transform
- Initial and Final Value Theorems
CHAPTER 8.....Discrete-Time Systems
- Difference Equations and the System Function
- Discrete-Time Frequency Response
- Delay-Adder-Gain Block Diagrams
- Describing a System
- Converting CT Systems to DT Systems
- Combining DT Systems
CHAPTER 9.....Generalized Functions
- The Impulse
- Derivatives of Discontinuities
- The Doublet
- Step Functions
- Properties
CHAPTER 10.....The Impulse Response and Convolution
- CT and DT Signals are Made of Impulses
- Definition of Impulse Response
- The Convolution Integral and Sum
- Eigenfunctions Revisited
- Links Between Time Domain and Frequency Domain
- Relation to Step Response
- Properties of Convolution
CHAPTER 11.....Discrete-Time Convolution
- Graphical Flip/Shift Method
- Convolving with Impulses
- Convolution Through Signal Decomposition
- Convolution of Infinite Length Signals
- Useful Checks
- Convolution Intuition
CHAPTER 12.....Continuous-Time Convolution
- Graphical Flip/Shift Method
- Convolution with Impulses
- Convolution by Inspection
- Useful Checks
- Matched Filters
CHAPTER 13.....Deconvolution
- What is Deconvolution?
- How to do Deconvolution
- Why is it useful?
- Potential Pitfalls
CHAPTER 14.....Causality and Stability
- What is Causality?
- Condition for Causality
- What is a Stable System?
- Conditions for Stability
CHAPTER 15.....Feedback
- What is Feedback?
- Positive versus Negative Feedback
- Black's Formula
- Loading Effects
- Using Feedback to Invert a System
- Accounting for System Fluctuations
- Removing System Nonlinearities
- Using Feedback to Stabilize Systems
- A Sample Problem
CHAPTER 16.....The Fourier Transform
- What is the Fourier Transform?
- Relationship to Bilateral Laplace Transform
- Fourier Transform Symmetry
- Fourier Transform Properties
- Parseval's Theorem and More
- Basic Fourier Transform Pairs
- Duration-Bandwidth and the Uncertainty Principle
- Fourier Transforms of Discrete Signals
- A Sample Problem
CHAPTER 17.....Filters
- What is Filtering?
- Types of Filters
- Non-Ideal Filters (the real world)
- Filter Terminology
- Designing a Continuous-Time Filter
- Circuit Realizations of Filters
- Recognizing a Filter
- A Visual Example
- Phase Response
- Digital Filters
- Switched-Capacitor Filters
CHAPTER 18.....Modulation
- What is Modulation?
- Amplitude Modulation
- Frequency Modulation and Phase Modulation
- Superheterodyne Receivers
- A Sample Problem
CHAPTER 19.....Sampling
- What is Sampling?
- Mechanisms of Sampling
- The Reconstruction Process
- Aliasing
- The Nyquist Sampling Theorem
- Practical Considerations
- A Sample Problem (no pun intended)
CHAPTER 20.....Fourier Series
- Orthogonal Basis Functions
- What is the Fourier Series?
- Forms of the Fourier Series
- Relationship Between the Fourier Series and Transform
- The DC Offset
- Properties of the Fourier Series Coefficients
- Parseval's Theorem for Fourier Series
- Square Wave Reconstruction
- A Sample Problem
APPENDIX.....Review Topics
- Complex Numbers
- Basic Linear Circuit Theory
- Quadratic Formula
- Trigonometric Identities
- Partial Fraction Expansion
- Logarithms
- Sequences and Series
- Binomial Expansion
- Linear Algebra
BIBLIOGRAPHY