A signal theoretic introduction to random processes / Roy M. Howard.

Format:

Book

Author/Creator:

Howard, Roy M., author.

Series:

New York Academy of Sciences Ser.

Language:

English

Subjects (All):

Random noise theory.

Signal processing.

Signal theory (Telecommunication).

Stochastic processes.

Physical Description:

1 online resource (742 p.)

Edition:

1st edition

Place of Publication:

Hoboken, New Jersey : Wiley, 2016.

Language Note:

English

System Details:

text file

Summary:

A fresh introduction to random processes utilizing signal theory By incorporating a signal theory basis, A Signal Theoretic Introduction to Random Processes presents a unique introduction to random processes with an emphasis on the important random phenomena encountered in the electronic and communications engineering field. The strong mathematical and signal theory basis provides clarity and precision in the statement of results. The book also features: A coherent account of the mathematical fundamentals and signal theory that underpin the presented material Unique, in-depth coverage of

Contents:

Title Page; Copyright Page; About the Author; Contents; Preface; Chapter 1 A Signal Theoretic Introduction to Random Processes; 1.1 INTRODUCTION; 1.2 MOTIVATION; 1.2.1 Usefulness of Randomness; 1.2.2 Engineering; 1.3 BOOK OVERVIEW; Chapter 2 Background: Mathematics; 2.1 INTRODUCTION; 2.2 SET THEORY; 2.2.1 Basic Definitions; 2.2.2 Infinity; 2.2.3 Supremum and Infimum; 2.3 FUNCTION THEORY; 2.3.1 Function Definition; 2.3.2 Common Functions; 2.3.3 Function Properties; 2.4 MEASURE THEORY; 2.4.1 Sigma Algebra; 2.4.2 Measure; 2.4.3 Lebesgue Measure; 2.5 MEASURABLE FUNCTIONS

2.5.1 Simple or Elementary Functions 2.6 LEBESGUE INTEGRATION; 2.6.1 The Lebesgue Integral; 2.6.2 Demarcation of Signal Space; 2.6.3 Miscellaneous Results; 2.7 CONVERGENCE; 2.7.1 Dominated and Monotone Convergence; 2.8 LEBESGUE-STIELTJES MEASURE; 2.8.1 Lebesgue-Stieltjes Measure: Monotonic Function Case; 2.8.2 Lebesgue-Stieltjes Measure: Decreasing Function; 2.8.3 Lebesgue-Stieltjes Measure: General Case; 2.9 LEBESGUE-STIELTJES INTEGRATION; 2.9.1 Motivation; 2.9.2 Lebesgue-Stieltjes Integral; 2.9.3 Lebesgue-Stieltjes Integrals: Specific Cases; 2.10 MISCELLANEOUS RESULTS; 2.11 PROBLEMS

APPENDIX 2.A PROOF OF THEOREM 2.1 APPENDIX 2.B PROOF OF THEOREM 2.2; APPENDIX 2.C PROOF OF THEOREM 2.7; APPENDIX 2.D PROOF OF THEOREM 2.8; APPENDIX 2.E PROOF OF THEOREM 2.10; Chapter 3 Background: Signal Theory; 3.1 INTRODUCTION; 3.2 SIGNAL ORTHOGONALITY; 3.2.1 Signal Decomposition; 3.2.2 Generalization; 3.2.3 Example: Hermite Basis Set; 3.3 THEORY FOR DIRICHLET POINTS; 3.3.1 Existence of Dirichlet Points; 3.4 DIRAC DELTA; 3.5 FOURIER THEORY; 3.5.1 Fourier Series; 3.5.2 Fourier Transform; 3.5.3 Inverse Fourier Transform; 3.5.4 Parsevalś Theorem; 3.6 SIGNAL POWER; 3.6.1 Sinusoidal Basis Set

3.6.2 Arbitrary Basis Set 3.7 THE POWER SPECTRAL DENSITY; 3.7.1 Energy Spectral Density; 3.7.2 Power Spectral Density: Sinusoidal Basis Set; 3.8 THE AUTOCORRELATION FUNCTION; 3.8.1 Definition of the Autocorrelation Function; 3.9 POWER SPECTRAL DENSITY-AUTOCORRELATION FUNCTION; 3.9.1 Relationships for Alternative Autocorrelation Function; 3.10 RESULTS FOR THE INFINITE INTERVAL; 3.10.1 Average Power; 3.10.2 The Power Spectral Density; 3.10.3 Integrated Spectrum; 3.10.4 Time Averaged Autocorrelation Function; 3.10.5 Power Spectral Density-Autocorrelation Relationship

3.11 CONVERGENCE OF FOURIER COEFFICIENTS 3.11.1 Periodic Signal Case; 3.11.2 Convergence of Fourier Coefficients to Zero; 3.12 Cramerś Representation and Transform; 3.12.1 Miscellaneous Mathematical Results; 3.12.2 Cramer Representation and Transform; 3.12.3 Initial Approach to the Cramer Transform; 3.12.4 The Cramer Transform; 3.12.5 Miscellaneous Results; 3.12.6 Transform of Common Signals; 3.12.7 Change in Transform; 3.12.8 Linear Filtering; 3.12.9 Integrated Spectrum, Spectrum, and Power Spectrum; 3.12.10 Cramer Transform of Standard Signals; 3.13 PROBLEMS

APPENDIX 3.A PROOF OF THEOREM 3.5

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on print version record.

ISBN:

9781119046790

1119046793

9781119046783

1119046785

OCLC:

918905879