### 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
• State Equations

### CHAPTER 3.....The Frequency Domain

• Why a New Domain?
• Complex Frequency
• Eigenfunctions
• An Example Problem
• Impedance

### 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
• 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
• 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
• 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