The origins of this book lie in our earlier book Random Processes: A Mathematical Approach for Engineers (Prentice Hall, 1986). This book began as a second edition to the earlier book and the basic goal remains unchanged – to introduce the fundamental ideas and mechanics of random processes to engineers in a way that accurately reflects the underlying mathematics, but does not require an extensive mathematical background and does not belabor detailed general proofs when simple cases suffice to get the basic ideas across. In the years since the original book was published, however, it has evolved into something bearing little resemblance to its ancestor. Numerous improvements in the presentation of the material have been suggested by colleagues, students, teaching assistants, and reviewers, and by our own teaching experience. The emphasis of the book shifted increasingly towards examples and a viewpoint that better reflected the title of the courses we taught using the book for many years at Stanford University and at the University of Maryland: An Introduction to Statistical Signal Processing. Much of the basic content of this course and of the fundamentals of random processes can be viewed as the analysis of statistical signal processing systems: typically one is given a probabilistic description for one random object, which can be considered as an input signal. An operation is applied to the input signal (signal processing) to produce a new random object, the output signal.