Introduction to random processes: with applications to signals and systems
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Macmillan
1986
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 434 S. Ill., graph. Darst. |
| ISBN: | 0029487900 |
Staff View
MARC
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| 100 | 1 | |a Gardner, William A. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Introduction to random processes |b with applications to signals and systems |c William A. Gardner |
| 264 | 1 | |a New York [u.a.] |b Macmillan |c 1986 | |
| 300 | |a XIII, 434 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Bruit | |
| 650 | 4 | |a Exercice processus stochastique | |
| 650 | 4 | |a Filtrage | |
| 650 | 4 | |a Filtre Kalman | |
| 650 | 4 | |a Filtre Wiener | |
| 650 | 4 | |a Modulation | |
| 650 | 4 | |a Processus Poisson | |
| 650 | 4 | |a Processus Wiener | |
| 650 | 4 | |a Processus stochastique | |
| 650 | 7 | |a Processus stochastiques |2 ram | |
| 650 | 4 | |a Signal | |
| 650 | 7 | |a Systèmes stochastiques |2 ram | |
| 650 | 4 | |a Théorie ergodique | |
| 650 | 7 | |a Traitement du signal |2 ram | |
| 650 | 4 | |a Signal processing | |
| 650 | 4 | |a Stochastic processes | |
| 650 | 4 | |a Stochastic systems | |
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Record in the Search Index
| _version_ | 1804116505276710912 |
|---|---|
| adam_text | Contents
PREFACE ix
PART 1: REVIEW OF PROBABILITY, RANDOM
VARIABLES, AND EXPECTATION 1
1 PROBABILITY AND RANDOM VARIABLES 3
1 1 The Notion of Probability 3
1 2 Sets 5
1 3 Sample Space 7
1 4 Probability Space 8
1 5 Conditional Probability 9
1 6 Independent Events 10
1 7 Random Variables 11
1 8 Probability Density 12
1 9 Functions of Random Variables 20
Exercises 22
2 EXPECTATION 26
2 1 The Notion of Expectation 26
2 2 Expected Value 27
2 3 Moments and Correlation 31
2 4 Conditional Expectation 37
2 5 Convergence 39
Exercises 44
FURTHER READING 48
v
vi • Contents
PART 2: RANDOM PROCESSES 50
3 INTRODUCTION TO RANDOM PROCESSES 51
3 1 Introduction 51
3 2 Generalized Harmonic Analysis 53
3 3 Signal-Processing Applications 61
3 4 Types of Random Processes 65
3 5 Summary 69
Exercises 70
4 MEAN AND AUTOCORRELATION 71
4 1 Definitions 71
4 2 Examples of Random Processes and Autocorrelations 72
4 3 Summary 78
Exercises 79
5 CLASSES OF RANDOM PROCESSES 82
5 1 Specification of Random Processes 82
5 2 Gaussian Processes 83
5 3 Markov Processes 84
5 4 Stationary Processes 92
5 5 Summary 99
Exercises 101
6 THE WIENER AND POISSON PROCESSES 108
6 1 Derivation of the Wiener Process 108
6 2 The Derivative of the Wiener Process 112
6 3 Derivation of the Poisson Process 113
6 4 The Derivative of the Poisson Counting Process 117
6 5 Marked and Filtered Poisson Processes 118
6 6 Summary 121
Exercises 122
7 STOCHASTIC CALCULUS 130
7 1 The Notion of a Calculus for Random Functions 130
7 2 Mean-Square Continuity 132
7 3 Mean-Square Differentiability 134
7 4 Mean-Square Integrability 136
7 5 Summary 138
Exercises 139
Contents • vii
8 ERGODICITY AND DUALITY 143
8 1 The Notion of Ergodicity 143
8 2 Discrete and Continuous Time Averages 146
8 3 Mean-Square Ergodicity of the Mean 148
8 4 Mean-Square Ergodicity of the Autocorrelation 150
8 5 Regular Processes 154
8 6 Duality and the Role of Ergodicity 159
8 7 Summary 161
Exercises 162
9 LINEAR TRANSFORMATIONS, FILTERS, AND
DYNAMICAL SYSTEMS 168
9 1 Linear Transformation of an A-tuple of Random Variables 168
9 2 Linear Discrete-Time Filtering 170
9 3 Linear Continuous-Time Filtering 174
9 4 Dynamical Systems 179
9 5 Summary 190
Exercises 191
10 SPECTRAL DENSITY 198
10 1 Input-Output Relations 198
10 2 Expected Spectral Density 204
10 3 Coherence 207
10 4 Time-Average Power Spectral Density and Duality 208
10 5 Spectral Density for Ergodic and Nonergodic Regular
Stationary Processes 209
10 6 Spectral Density for Regular Nonstationary Processes 210
10 7 White Noise 213
10 8 Bandwidths 222
10 9 Spectral Lines 223
10 10 Summary 224
Exercises 226
11 SPECIAL TOPICS AND APPLICATIONS 238
11 1 Sampling and Pulse Modulation 238
11 2 Bandpass Processes 244
11 3 Frequency Modulation and Demodulation 251
11 4 PSD Measurement Analysis 260
11 5 Noise Modeling for Receiving Systems 264
viii • Contents
11 6 Matched Filtering and Signal Detection 269
11 7 Wiener Filtering and Signal Extraction 272
11 8 Random-Signal Detection 274
11 9 Autoregressive Models and Linear Prediction 278
11 10 Summary 287
Exercises 288
12 CYCLOSTATION ARY PROCESSES 301
12 1 Introduction 301
12 2 Cyclic Autocorrelation and Cyclic Spectrum 302
12 3 Stationary and Cyclostationary Components 310
12 4 Linear Periodically Time-Variant Transformations 312
12 5 Examples of Cyclic Spectra for Modulated Signals 324
12 6 Stationary Representations 341
12 7 Cycloergodicity and Duality 345
12 8 Applications 349
12 9 Summary 352
Exercises 354
13 MINIMUM-MEAN-SQUARED-ERROR ESTIMATION 360
13 1 The Notion of Minimum-Mean-Squared-Error Estimation 360
13 2 Geometric Foundations 362
13 3 Minimum-Mean-Squared-Error Estimation 371
13 4 Noncausal Wiener Filtering 378
13 5 Causal Wiener Filtering 386
13 6 Kalman Filtering 395
13 7 Optimum Periodically Time-Variant Filtering 405
13 8 Summary 408
Exercises 409
REFERENCES 419
AUTHOR INDEX 425
|
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| discipline | Mathematik |
| format | Book |
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| isbn | 0029487900 |
| language | English |
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| spelling | Gardner, William A. Verfasser aut Introduction to random processes with applications to signals and systems William A. Gardner New York [u.a.] Macmillan 1986 XIII, 434 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Bruit Exercice processus stochastique Filtrage Filtre Kalman Filtre Wiener Modulation Processus Poisson Processus Wiener Processus stochastique Processus stochastiques ram Signal Systèmes stochastiques ram Théorie ergodique Traitement du signal ram Signal processing Stochastic processes Stochastic systems Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content Stochastischer Prozess (DE-588)4057630-9 s DE-604 HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001343957&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Gardner, William A. Introduction to random processes with applications to signals and systems Bruit Exercice processus stochastique Filtrage Filtre Kalman Filtre Wiener Modulation Processus Poisson Processus Wiener Processus stochastique Processus stochastiques ram Signal Systèmes stochastiques ram Théorie ergodique Traitement du signal ram Signal processing Stochastic processes Stochastic systems Stochastischer Prozess (DE-588)4057630-9 gnd |
| subject_GND | (DE-588)4057630-9 (DE-588)4151278-9 |
| title | Introduction to random processes with applications to signals and systems |
| title_auth | Introduction to random processes with applications to signals and systems |
| title_exact_search | Introduction to random processes with applications to signals and systems |
| title_full | Introduction to random processes with applications to signals and systems William A. Gardner |
| title_fullStr | Introduction to random processes with applications to signals and systems William A. Gardner |
| title_full_unstemmed | Introduction to random processes with applications to signals and systems William A. Gardner |
| title_short | Introduction to random processes |
| title_sort | introduction to random processes with applications to signals and systems |
| title_sub | with applications to signals and systems |
| topic | Bruit Exercice processus stochastique Filtrage Filtre Kalman Filtre Wiener Modulation Processus Poisson Processus Wiener Processus stochastique Processus stochastiques ram Signal Systèmes stochastiques ram Théorie ergodique Traitement du signal ram Signal processing Stochastic processes Stochastic systems Stochastischer Prozess (DE-588)4057630-9 gnd |
| topic_facet | Bruit Exercice processus stochastique Filtrage Filtre Kalman Filtre Wiener Modulation Processus Poisson Processus Wiener Processus stochastique Processus stochastiques Signal Systèmes stochastiques Théorie ergodique Traitement du signal Signal processing Stochastic processes Stochastic systems Stochastischer Prozess Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001343957&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT gardnerwilliama introductiontorandomprocesseswithapplicationstosignalsandsystems |