Probability and Random Processes with Applications to Signal Processing, 3/e (精裝)

For courses in Probability and Random Processes.

This book is a comprehensive treatment of probability and random processes that, more than any other available source, combines rigor with accessibility. Beginning with the fundamentals of probability theory and requiring only college-level calculus, the book develops all the tools needed to understand more advanced topics such as random sequences (Chapter 6), continuous-time random processes (Chapter 7), and statistical signal processing (Chapter 9). The book progresses at a leisurely pace, never assuming more knowledge than contained in the material already covered. Rigor is established by developing all results from the basic axioms (Chapters 1,2) and carefully defining and discussing such advanced notions as stochastic convergence, stochastic integrals and resolution of stochastic processes (Chapter 8). The 3rd Edition has a large number of new topics, not present in the 2nd Edition, including additional material on basic probability (Appendix B, Section 1.8, Section 1.11), statistics (chi-square and Student-t in Section 2.4, Section 4.1), misuses of probability (Sec. 1.3), and signal processing (all of Chapter 9).

Table of Contents

1. Introduction to Probability.
2. Random Variables.
3. Functions of Random Variables.
4. Expectation and Introduction to Estimation.
5. Random Vectors and Parameter Estimation.
6. Random Sequences.
7. Random Processes.
8. Advanced Topics in Random Processes.
9. Applications to Statistical Signal Processing.
Appendices.
Appendix A: Review of Relevant Mathematics.
Appendix B: Gamma and Delta Functions.
Appendix C: Functional Transformations and Jacobians.
Appendix D: Measure and Probability.
Appendix E: Sampled Analog Waveforms and Discrete-time Signals.