EE120UCB

Table of contents

1. 1 Signals and Systems
2. 2 Defining Signals and Systems
3. 3 State Machines
4. 4 Composing State Machines
5. 5 Linear Systems
6. 6 Hybrid Systems
7. 7 Frequency Domain
8. 8 Frequency Response
9. 9 Filtering
10. 10 The Four Fourier Transforms
11. 11 Sampling and Reconstruction
12. 12 Stability
13. 13 Laplace and Z Transforms
14. 14 Composition and Feedback Control
15. A Sets and Functions
16. B Complex Numbers

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1 Signals and Systems

• 1.1 Signals
• 1.2 Systems
• 1.3 Summary
• Exercises

2 Defining Signals and Systems

• 2.1 Defining functions
• 2.2 Defining signals
• 2.3 Defining systems
• 2.4 Summary
• Exercises

3 State Machines

• 3.1 Structure of state machines
• 3.2 Finite state machines
• 3.3 Nondeterministic state machines
• 3.4 Simulation relations
• 3.5 Summary
• Exercises

4 Composing State Machines

• 4.1 Synchrony
• 4.2 Side-by-side composition
• 4.3 Cascade composition
• 4.4 Product-form inputs and outputs
• 4.5 General feedforward composition
• 4.6 Hierarchical composition
• 4.7 Feedback
• 4.8 Summary
• Exercises

5 Linear Systems

• 5.1 Operation of an infinite state machine
• 5.2 Linear functions
• 5.3 The [A,B,C,D] representation of a system
• 5.4 Continuous-time state-space models
• 5.5 Summary
• Exercises

6 Hybrid Systems

• 6.1 Mixed models
• 6.2 Modal models
• 6.3 Timed automata
• 6.4 More interesting dynamics
• 6.5 Supervisory control
• 6.6 Formal model
• 6.7 Summary
• Exercises

7 Frequency Domain

• 7.1 Frequency decomposition
• 7.2 Phase
• 7.3 Spatial frequency
• 7.4 Periodic and finite signals
• 7.5 Fourier series
• 7.6 Discrete-time signals
• 7.7 Summary
• Exercises

8 Frequency Response

• 8.1 LTI systems
• 8.2 Finding and using the frequency response
• 8.3 Determining the Fourier series coefficients
• 8.4 Frequency response and the Fourier series
• 8.5 Frequency response of composite systems
• 8.6 Summary
• Exercises

9 Filtering

• 9.1 Convolution
• 9.2 Frequency response and impulse response
• 9.3 Causality
• 9.4 Finite impulse response (FIR) filters
• 9.5 Infinite impulse response (IIR) filters
• 9.6 Implementation of filters
• 9.7 Summary
• Exercises

10 The Four Fourier Transforms

• 10.1 Notation
• 10.2 The Fourier series (FS)
• 10.3 The discrete Fourier transform (DFT)
• 10.4 The discrete-Time Fourier transform (DTFT)
• 10.5 The continuous-time Fourier transform
• 10.6 Fourier transforms vs. Fourier series
• 10.7 Properties of Fourier transforms
• 10.8 Summary
• Exercises

11 Sampling and Reconstruction

• 11.1 Sampling
• 11.2 Reconstruction
• 11.3 The Nyquist-Shannon sampling theorem
• 11.4 Summary
• Exercises

12 Stability

• 12.1 Boundedness and stability
• 12.2 The Z transform
• 12.3 The Laplace transform
• 12.4 Summary
• Exercises

13 Laplace and Z Transforms

• 13.1 Properties of the Z tranform
• 13.2 Frequency response and pole-zero plots
• 13.3 Properties of the Laplace transform
• 13.4 Frequency response and pole-zero plots
• 13.5 The inverse transforms
• 13.6 Steady state response
• 13.7 Linear difference and differential equations
• 13.8 State-space models
• 13.9 Summary
• Exercises

14 Composition and Feedback Control

• 14.1 Cascade composition
• 14.2 Parallel composition
• 14.3 Feedback composition
• 14.4 PID controllers
• 14.5 Summary
• Exercises

A Sets and Functions

• A.1 Sets
• A.2 Functions
• A.3 Summary
• Exercises

B Complex Numbers

• B.1 Imaginary numbers
• B.2 Arithmetic of imaginary numbers
• B.3 Complex numbers
• B.4 Arithmetic of complex numbers
• B.5 Exponentials
• B.6 Polar coordinates
• Exercises

Bibliography

Notation Index

Index