A First Course in Statistics for Signal Analysis

Wojbor A. Woyczynski

May 2007 · Springer Science & Business Media

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This book was designed as a text for a ?rst, one-semester course in s- tisticalsignalanalysisforstudentsinengineeringandphysicalsciences. It had been developed over the last few years as lecture notes used by theauthorinclassesmainlypopulatedbyelectrical, systems, computer and biomedical engineering juniors/seniors and graduate students in sciences and engineering who have not been previously exposed to this material. It was also used for industrial audiences as educational and training material and for an introductory time series analysis class. Theonlyprerequisiteforthiscourseisabasictwo-tothree-semester calculus sequence; no probability or statistics background is assumed except the usual high school elementary introduction. The emphasis is on a crisp and concise but fairly rigorous presentation of fundamental concepts in the statistical theory of stationary random signals and re- tionships between them. The author’s goal was to write a compact but readable book of approximately 200 pages countering the recent trend towards fatter and fatter textbooks. Since Fourier series and transforms are of fundamental importance in random signal analysis and processing, this material is developed from scratch in Chapter 2 emphasizing the time domain vs. frequency domain duality. Our experience showed that although harmonic an- ysis is normally included in the calculus syllabi, students’ practical - derstanding of its concepts is often hazy. Chapter 3 introduces basic conceptsofprobabilitytheory,lawoflargenumbersandthestabilityof ?uctuations law, and statistical parametric inference procedures based on the latter.