TABLE OF CONTENTS

1. Signals and Systems.
1.1 Signals
1.2 Systems
1.3 Summary

2. Defining Signals and Systems.
2.1 Defining functions
2.2 Defining signals
2.3 Defining systems
2.4 Summary

3. State Machines.
3.1 Structures and state machines
3.2 Finite-state machines
3.3 Nondeterministic state macines
3.4 Simulation and bisimulations
3.5 Summary

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 feed-forward composition
4.6 Hierachical composition
4.7 Feedback
4.8 Summary

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 discrete linear system
5.4 Continuous-time state-space models
5.5 Summary

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

7. Frequency Domain.
7.1 Frequency decompositino
7.2 Phase
7.3 Spatial frequency
7.4 Periodic and finite signals
7.5 Fourier series
7.6 Disctrete-time signals
7.7 Summary

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

9. Filtering.
9.1 Convolution
9.2 Frequency response and impulse response
9.3 Causality
9.4 Finite impulse response filters
9.5 Infinite impulse response (IIR) filters
9.6 Implementation of filters
9.7 Summary

10. The Four Fourier Transforms.
10.1 Notation
10.2 The Fourier series
10.3 The discrete Fourier transformation
10.4 The discrete-time Fourier transformation
10.5 The continuous-time Fourier transformation
10.6 Fourier transforms versus Fourier series
10.7 Properties of Fourier transforms
10.8 Summary

11. Sampling and Reconstruction.
11.1 Sampling
11.2 Reconstruction
11.3 The Nyquist-Shannon sampling
11.4 Summary

12. Stability.
12.1 Boundedness and stability
12.2 The Z transform
12.3 The Laplace transform
12.4 Summary

13. Laplace and Z Transforms.
13.1 Properties of the Z transform
13.2 Frequency response and pole-zero plots
13.3 Properties of the Laplace transform
13.4 Frequency response and pole-zero plots, continuous time
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

14. Composition and Feedback Control.
14.1 Cascade composition
14.2 Parallel composition
14.3 Feedback composition
14.4 PID controllers
14.5 Summary

Appendix A: Sets and Functions.
Appendix B: Complex Numbers.