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Produktbild: A Signal Theoretic Introduction to Random Processes

A Signal Theoretic Introduction to Random Processes

158,99 €

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Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

27.07.2015

Verlag

John Wiley & Sons Inc

Seitenzahl

744

Maße (L/B/H)

23,6/16/4,3 cm

Gewicht

1134 g

Auflage

1. Auflage

Sprache

Englisch

ISBN

978-1-119-04677-6

Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

27.07.2015

Verlag

John Wiley & Sons Inc

Seitenzahl

744

Maße (L/B/H)

23,6/16/4,3 cm

Gewicht

1134 g

Auflage

1. Auflage

Sprache

Englisch

ISBN

978-1-119-04677-6

Herstelleradresse

Libri GmbH
Europaallee 1
36244 Bad Hersfeld
DE

Email: gpsr@libri.de

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  • Produktbild: A Signal Theoretic Introduction to Random Processes
  • Preface xiii
     
    1 A Signal Theoretic Introduction to Random Processes 1
     
    1.1 Introduction 1
     
    1.2 Motivation 2
     
    1.3 Book Overview 8
     
    2 Background: Mathematics 11
     
    2.1 Introduction 11
     
    2.2 Set Theory 11
     
    2.3 Function Theory 13
     
    2.4 Measure Theory 18
     
    2.5 Measurable Functions 24
     
    2.6 Lebesgue Integration 28
     
    2.7 Convergence 37
     
    2.8 Lebesgue-Stieltjes Measure 39
     
    2.9 Lebesgue-Stieltjes Integration 50
     
    2.10 Miscellaneous Results 61
     
    2.11 Problems 62
     
    3 Background: Signal Theory 71
     
    3.1 Introduction 71
     
    3.2 Signal Orthogonality 71
     
    3.3 Theory for Dirichlet Points 75
     
    3.4 Dirac Delta 78
     
    3.5 Fourier Theory 79
     
    3.6 Signal Power 82
     
    3.7 The Power Spectral Density 84
     
    3.8 The Autocorrelation Function 91
     
    3.9 Power Spectral Density-Autocorrelation Function 95
     
    3.10 Results for the Infinite Interval 96
     
    3.11 Convergence of Fourier Coefficients 103
     
    3.12 Cramer's Representation and Transform 106
     
    3.13 Problems 125
     
    4 Background: Probability and Random Variable Theory 153
     
    4.1 Introduction 153
     
    4.2 Basic Concepts: Experiments-Probability Theory 153
     
    4.3 The Random Variable 160
     
    4.4 Discrete and Continuous Random Variables 162
     
    4.5 Standard Random Variables 165
     
    4.6 Functions of a Random Variable 165
     
    4.7 Expectation 166
     
    4.8 Generation of Data Consistent with Defined PDF 172
     
    4.9 Vector Random Variables 173
     
    4.10 Pairs of Random Variables 175
     
    4.11 Covariance and Correlation 186
     
    4.12 Sums of Random Variables 191
     
    4.13 Jointly Gaussian Random Variables 193
     
    4.14 Stirling's Formula and Approximations to Binomial 194
     
    4.15 Problems 199
     
    5 Introduction to Random Processes 219
     
    5.1 Random Processes 219
     
    5.2 Definition of a Random Process 219
     
    5.3 Examples of Random Processes 221
     
    5.4 Experiments and Experimental Outcomes 225
     
    5.5 Prototypical Experiments 228
     
    5.6 Random Variables Defined by a Random Process 232
     
    5.7 Classification of Random Processes 233
     
    5.8 Classification: One-Dimensional RPs 236
     
    5.9 Sums of Random Processes 239
     
    5.10 Problems 239
     
    6 Prototypical Random Processes 243
     
    6.1 Introduction 243
     
    6.2 Bernoulli Random Processes 243
     
    6.3 Poisson Random Processes 246
     
    6.4 Clustered Random Processes 255
     
    6.5 Signalling Random Processes 257
     
    6.6 Jitter 262
     
    6.7 White Noise 265
     
    6.8 1/f Noise 272
     
    6.9 Birth-Death Random Processes 275
     
    6.10 Orthogonal Increment Random Processes 278
     
    6.11 Linear Filtering of Random Processes 282
     
    6.12 Summary of Random Processes 283
     
    6.13 Problems 285
     
    7 Characterizing Random Processes 289
     
    7.1 Introduction 289
     
    7.2 Time Evolution of PMF or PDF 291
     
    7.3 First-, Second-, and Higher-Order Characterization 292
     
    7.4 Autocorrelation and Power Spectral Density 297
     
    7.5 Correlation 308
     
    7.6 Notes on Average Power and Average Energy 310
     
    7.7 Classification: Stationarity vs Non-Stationarity 316
     
    7.8 Cramer's Representation 323
     
    7.9 State Space Characterization of Random Processes 335
     
    7.10 Time Series Characterization 347
     
    7.11 Problems 347
     
    8 PMF and PDF Evolution 369
     
    8.1 Introduction 369
     
    8.2 Probabili