LEADER 05830nam 2200817 450 001 9910797205803321 005 20231110225859.0 010 $a1-119-04679-3 010 $a1-119-04678-5 035 $a(CKB)3710000000443966 035 $a(EBL)1895995 035 $a(SSID)ssj0001515666 035 $a(PQKBManifestationID)12621979 035 $a(PQKBTitleCode)TC0001515666 035 $a(PQKBWorkID)11481791 035 $a(PQKB)11185485 035 $a(PQKBManifestationID)16039790 035 $a(PQKB)22271861 035 $a(DLC) 2014050055 035 $a(Au-PeEL)EBL1895995 035 $a(CaPaEBR)ebr11076354 035 $a(CaONFJC)MIL812241 035 $a(OCoLC)918905879 035 $a(Au-PeEL)EBL7104377 035 $a(CaSebORM)9781119046776 035 $a(MiAaPQ)EBC1895995 035 $a(JP-MeL)3000110593 035 $a(MiAaPQ)EBC7104377 035 $a(EXLCZ)993710000000443966 100 $a20150724h20162016 uy 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt 182 $cc 183 $acr 200 12$aA signal theoretic introduction to random processes /$fRoy M. Howard 205 $a1st edition 210 1$aHoboken, New Jersey :$cWiley,$d2016. 210 4$d2016 215 $a1 online resource (742 p.) 225 1 $aNew York Academy of Sciences 300 $aIncludes bibliographical references and index 311 $a1-119-04677-7 320 $aIncludes bibliographical references and index. 327 $aTitle 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 327 $a2.5.1 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 327 $aAPPENDIX 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 Parsevals? Theorem; 3.6 SIGNAL POWER; 3.6.1 Sinusoidal Basis Set 327 $a3.6.2 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 327 $a3.11 CONVERGENCE OF FOURIER COEFFICIENTS 3.11.1 Periodic Signal Case; 3.11.2 Convergence of Fourier Coefficients to Zero; 3.12 Cramers? 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 327 $aAPPENDIX 3.A PROOF OF THEOREM 3.5 330 $aA fresh introduction to random processes utilizing signal theory By incorporating a signal theory basis, A Signal Theoretic Introduction to Random Processes presents a unique introduction to random processes with an emphasis on the important random phenomena encountered in the electronic and communications engineering field. The strong mathematical and signal theory basis provides clarity and precision in the statement of results. The book also features: A coherent account of the mathematical fundamentals and signal theory that underpin the presented material Unique, in-depth coverage of 410 0$aNew York Academy of Sciences 606 $aSignal processing 606 $aSignal theory (Telecommunication) 606 $aStochastic processes 606 $aRandom noise theory 615 0$aSignal processing. 615 0$aSignal theory (Telecommunication) 615 0$aStochastic processes. 615 0$aRandom noise theory. 676 $a003.54 686 $a547.1$2njb/09 686 $a003/.54$2njb/09 700 $aHoward$b Roy M.$0322948 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910797205803321 996 $aA signal theoretic introduction to random processes$93732849 997 $aUNINA