05830nam 2200817 450 991081144340332120231110225859.01-119-04679-31-119-04678-5(CKB)3710000000443966(EBL)1895995(SSID)ssj0001515666(PQKBManifestationID)12621979(PQKBTitleCode)TC0001515666(PQKBWorkID)11481791(PQKB)11185485(PQKBManifestationID)16039790(PQKB)22271861(DLC) 2014050055(Au-PeEL)EBL1895995(CaPaEBR)ebr11076354(CaONFJC)MIL812241(OCoLC)918905879(Au-PeEL)EBL7104377(CaSebORM)9781119046776(MiAaPQ)EBC1895995(JP-MeL)3000110593(MiAaPQ)EBC7104377(EXLCZ)99371000000044396620150724h20162016 uy 0engur|||||||||||txtccrA signal theoretic introduction to random processes /Roy M. Howard1st editionHoboken, New Jersey :Wiley,2016.20161 online resource (742 p.)New York Academy of Sciences Includes bibliographical references and index1-119-04677-7 Includes bibliographical references and index.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 FUNCTIONS2.5.1 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 PROBLEMSAPPENDIX 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 Set3.6.2 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 Relationship3.11 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 PROBLEMSAPPENDIX 3.A PROOF OF THEOREM 3.5A 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 ofNew York Academy of Sciences Signal processingSignal theory (Telecommunication)Stochastic processesRandom noise theorySignal processing.Signal theory (Telecommunication)Stochastic processes.Random noise theory.003.54547.1njb/09003/.54njb/09Howard Roy M.322948MiAaPQMiAaPQMiAaPQBOOK9910811443403321A signal theoretic introduction to random processes3927848UNINA