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A First Course in Statistics for Signal Analysis

  • Textbook
  • © 2006

Overview

Authors:
  1. Wojbor A. Woyczyński

    1. Department of Statistics and Center for Stochastic and Chaotic Processes in Science and Technology, Case Western Reserve University, Cleveland, USA

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    You can also search for this author in PubMed   Google Scholar

  • Self-contained, deliberately compact, and user-friendly textbook
  • Many diverse examples as well as end-of-chapter problems and exercises
  • Computer simulation algorithms to reinforce the theory presented
  • Accessible to a broad audience of junior/senior undergraduates or graduate students in electrical, systems, computer, and biomedical engineering, as well as the physical sciences

  • 13k Accesses

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Description of Signals

    Pages 1-15

  3. Spectral Representation of Deterministic Signals: Fourier Series and Transforms

    Pages 17-46

  4. Random Quantities and Random Vectors

    Pages 47-92

  5. Stationary Signals

    Pages 93-111

  6. Power Spectra of Stationary Signals

    Pages 113-126

  7. Transmission of Stationary Signals through Linear Systems

    Pages 127-146

  8. Optimization of Signal-to-Noise Ratio in Linear Systems

    Pages 147-157

  9. Gaussian Signals, Correlation Matrices, and Sample Path Properties

    Pages 159-174

  10. Discrete Signals and Their Computer Simulations

    Pages 175-196

  11. Back Matter

    Pages 197-207
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About this book

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.

Reviews

“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 is targeted at classes ‘mainly populated by electrical, systems, computer and biomedical engineering juniors/seniors and graduate students…’ 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, A First Course in Statistics for Signal Analysis has much in its favor. It is short, rigorous, mostly free of typos, and inexpensive…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

Authors and Affiliations

  • Department of Statistics and Center for Stochastic and Chaotic Processes in Science and Technology, Case Western Reserve University, Cleveland, USA

    Wojbor A. Woyczyński

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