First Course in Statistics for Signal Analysis

'A First Course in Statistics for Signal Analysis' is a small, dense, and inexpensive book that covers exactly what the title says: statistics for signal analysis. The book has much to recommend it. The author clearly understands the topics presented. The topics are covered in a rigorous manner, but not so rigorous as to be ostentatious. The sequence of topics is clearly targeted at the spectral properties of Gaussian stationary signals. Any student studying traditional communications and signal processing would benefit from an understanding of these topics ... In summary, [the work] has much in its favor ... This book is most appropriate for a graduate class in signal analysis. It also could be used as a secondary text in a statistics, signal processing, or communications class. --JASA (Review of the First Edition) This essentially self-contained, deliberately compact, and user-friendly textbook is designed for a first, one-semester course in statistical signal analysis for a broad audience of students in engineering and the physical sciences. The emphasis throughout is on fundamental concepts and relationships in the statistical theory of stationary random signals, explained in a concise, yet fairly rigorous presentation. Topics and Features: Fourier series and transforms--fundamentally important in random signal analysis and processing--are developed from scratch, emphasizing the time-domain vs. frequency-domain duality; Basic concepts of probability theory, laws of large numbers, the central limit theorem, and statistical parametric inference procedures are presented so that no prior knowledge of probability and statistics is required; the only prerequisite is a basic two-three semester calculus sequence; Computer simulation algorithms of stationary random signals with a given power spectrum density; Complementary bibliography for readers who wish to pursue the study of random signals in greater depth; Many diverse examples and end-of-chapter problems and exercises. New to the Second Edition: Revised notation and terminology to better reflect the concepts under discussion; Many redrawn figures to better illustrate the scale of the quantities represented; Considerably expanded sections with new examples, illustrations, and commentary; Addition of more applied exercises; A large appendix containing solutions of selected problems from each of the nine chapters. Developed by the author over the course of many years of classroom use, A First Course in Statistics for Signal Analysis, Second Edition may be used by junior/senior undergraduates or graduate students in electrical, systems, computer, and biomedical engineering, as well as the physical sciences. The work is also an excellent resource of educational and training material for scientists and engineers working in research laboratories.

""9.3 Stochastic Integration with Respect to Signals with Uncorrelated Increments""

""A First Course in Statistics for Signal Analysis""; ""Contents ""; ""Foreword to the Second Edition""; ""Introduction""; ""Notation""; ""1 Description of Signals""; ""1.1 Types of Random Signals""; ""1.2 Characteristics of Signals""; ""1.3 Time-Domain and Frequency-Domain Descriptions of Periodic Signals""; ""1.4 Building a Better Mousetrap: Complex Exponentials""; ""1.5 Problems and Exercises""; ""2 Spectral Representation of Deterministic Signals: Fourier Series and Transforms""; ""2.1 Complex Fourier Series for Periodic Signals""

""2.2 Approximation of Periodic Signals by Finite Fourier Sums""""2.3 Aperiodic Signals and Fourier Transforms""; ""2.4 Basic Properties of the Fourier Transform""; ""2.5 Fourier Transforms of Some Nonintegrable Signals; Dirac's Delta Impulse""; ""2.6 Discrete and Fast Fourier Transforms""; ""2.7 Problems and Exercises""; ""3 Random Quantities and Random Vectors""; ""3.1 Discrete, Continuous, and Singular Random Quantities""; ""3.2 Expectations and Moments of Random Quantities""; ""3.3 Random Vectors, Conditional Probabilities, Statistical Independence, and Correlations""

""3.4 The Least-Squares Fit, Linear Regression""""3.5 The Law of Large Number…