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A First Course in Statistics for Signal Analysis

A First Course in Statistics for Signal Analysis This self-contained, deliberately compact, and user-friendly book 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. Developed by the author over the course of several years of classroom use, this book may be used by junior/senior undergraduates or graduate students in electrical, systems, computer, and biomedical engineering, as well as the physical sciences. ; This user-friendly book is designed for a first, one-semester course in statistical signal analysis for a broad audience of students in engineering and the physical sciences. A bibliography is included for readers who wish to pursue things in greater depth. ; 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.; Introduction Notation Description of Signals Spectral Representation of Deterministic Signals: Fourier Series and Transforms Random Quantities and Random Vectors Stationary Signals Power Spectra of Stationary Signals Transmission of Stationary Signals through Linear Systems Optimization of Signal-to-Noise Ratio in Linear Systems Gaussian Signals, Correlation Matrices, and Sample Path Properties Discrete Signals and Their Computer Simulations Bibliographical Comments; “ 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 ; 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 stability of fluctuations law (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. *Introduction of the fundamental concept of a stationary random signal and its autocorrelation structure. *Power spectra of stationary signals and transmission analysis. *Filter design with optimal signal-to-noise ratio. *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 as well as end-of-chapter problems and exercises. Developed by the author over the course of several years of classroom use, A First Course in Statistics for Signal Analysis 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. ; 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 ; 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. Developed by the author over the course of several years of classroom use, A First Course in Statistics for Signal Analysis 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 materials for scientists working in research laboratories. ; US http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

A First Course in Statistics for Signal Analysis

Woyczynski, Wojbor
Springer E-books — May 26, 2007
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216 pages

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Publisher
Birkhäuser Boston
Copyright
Copyright � Springer Basel AG
DOI
10.1007/978-0-8176-4516-8
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Abstract

This self-contained, deliberately compact, and user-friendly book 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. Developed by the author over the course of several years of classroom use, this book may be used by junior/senior undergraduates or graduate students in electrical, systems, computer, and biomedical engineering, as well as the physical sciences. ; This user-friendly book is designed for a first, one-semester course in statistical signal analysis for a broad audience of students in engineering and the physical sciences. A bibliography is included for readers who wish to pursue things in greater depth. ; 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.; Introduction Notation Description of Signals Spectral Representation of Deterministic Signals: Fourier Series and Transforms Random Quantities and Random Vectors Stationary Signals Power Spectra of Stationary Signals Transmission of Stationary Signals through Linear Systems Optimization of Signal-to-Noise Ratio in Linear Systems Gaussian Signals, Correlation Matrices, and Sample Path Properties Discrete Signals and Their Computer Simulations Bibliographical Comments; “ 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 ; 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 stability of fluctuations law (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. *Introduction of the fundamental concept of a stationary random signal and its autocorrelation structure. *Power spectra of stationary signals and transmission analysis. *Filter design with optimal signal-to-noise ratio. *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 as well as end-of-chapter problems and exercises. Developed by the author over the course of several years of classroom use, A First Course in Statistics for Signal Analysis 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. ; 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 ; 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. Developed by the author over the course of several years of classroom use, A First Course in Statistics for Signal Analysis 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 materials for scientists working in research laboratories. ; US

Published: May 26, 2007

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