Probability and random processes with applications to signal processing and communications
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Amsterdam [u.a.]
Elsevier Academic Press
2012
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| Ausgabe: | 2. ed. |
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| LEADER | 00000nam a2200000zc 4500 | ||
|---|---|---|---|
| 001 | BV040491584 | ||
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| 005 | 20121114 | ||
| 007 | t| | ||
| 008 | 121018s2012 xxua||| |||| 00||| eng d | ||
| 010 | |a 2011053022 | ||
| 020 | |a 9780123869814 |c alk. paper |9 978-0-12-386981-4 | ||
| 020 | |a 0123869811 |c alk. paper |9 0-12-386981-1 | ||
| 035 | |a (OCoLC)794668964 | ||
| 035 | |a (DE-599)BVBBV040491584 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 044 | |a xxu |c US | ||
| 049 | |a DE-473 |a DE-B768 | ||
| 050 | 0 | |a TK5102.9 | |
| 082 | 0 | |a 621.382/20151 | |
| 084 | |a ST 306 |0 (DE-625)143654: |2 rvk | ||
| 100 | 1 | |a Miller, Scott L. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Probability and random processes |b with applications to signal processing and communications |c Scott L. Miller, Donald Childers |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Amsterdam [u.a.] |b Elsevier Academic Press |c 2012 | |
| 300 | |a xii, 611 p. |b ill. |c 25 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Signal processing |x Mathematics | |
| 650 | 4 | |a Probabilities | |
| 650 | 4 | |a Stochastic processes | |
| 650 | 0 | 7 | |a Wahrscheinlichkeitstheorie |0 (DE-588)4079013-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Sprachverarbeitung |0 (DE-588)4116579-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Stochastischer Prozess |0 (DE-588)4057630-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Sprachverarbeitung |0 (DE-588)4116579-2 |D s |
| 689 | 0 | 1 | |a Wahrscheinlichkeitstheorie |0 (DE-588)4079013-7 |D s |
| 689 | 0 | 2 | |a Stochastischer Prozess |0 (DE-588)4057630-9 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Childers, Donald G. |e Verfasser |4 aut | |
| 856 | 4 | 2 | |m Digitalisierung UB Bamberg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025338565&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-025338565 | |
Datensatz im Suchindex
| _version_ | 1819698217199075328 |
|---|---|
| adam_text | Contents
Preface
..............................................................................................................xi
Chapter
1:
Introduction
......................................................................................1
1.1
A Speech Recognition System
.............................................................................2
1.2
A Radar System
....................................................................................................4
1.3
A Communication Network
..................................................................................4
Chapter
2:
Introduction to Probability Theory
.......................................................7
2.1
Experiments, Sample Spaces, and Events
............................................................7
2.2
Axioms of Probability
.........................................................................................10
2.3
Assigning Probabilities
........................................................................................13
2.4
Joint and Conditional Probabilities
.....................................................................17
2.5
Basic Combinatorics
............................................................................................20
2.6
Bayes s
Theorem
.................................................................................................27
2.7
Independence
.......................................................................................................29
2.8
Discrete Random Variables
.................................................................................32
2.9
Engineering Application
—
An Optical Communication System
.........................38
Exercises
..............................................................................................................43
MATLAB
Exercises
............................................................................................61
Chapter
3:
Random Variables, Distributions, and Density Functions
.....................63
3.1
The Cumulative Distribution Function
................................................................64
3.2
The Probability Density Function
........................................................................69
3.3
The Gaussian Random Variable
..........................................................................71
3.4
Other Important Random Variables
....................................................................78
3.4.1
Uniform Random Variable
.............................................................................78
3.4.2
Exponential Random Variable
...........,..........................................................79
3.4.3
Laplace Random Variable
.............................................................................80
3.4.4
Gamma Random Variable
..........................................................,..................81
3.4.5
Erlang
Random Variable
............................................................................... 81
3.4.6
Chi-Squamd Random Variable
.....................................................................82
3.4.7
Rayleigh Random Variable
...........................................................................82
3.4.8
Ridan
Random Variable
...............................................................................83
3.4.9
Cauchy Random Variable
.............................................................................84
vi
Contents
3.5
Conditional Distribution and Density Functions
................................................85
3.6
Engineering Application: Reliability and Failure Rates
.....................................91
Exercises
.............................................................................................................97
MATLAB
Exercises
..........................................................................................
Ю9
Chapter
4:
Operations on a Single Random Variable
..........................................111
4.1
Expected Value of a Random Variable
.............................................................
HI
4.2
Expected Values of Functions of Random Variables
.......................................113
4.3
Moments
...........................................................................................................115
4.4
Central Moments
...............................................................................................117
4.5
Conditional Expected Values
............................................................................121
4.6
Transformations of Random Variables
.............................................................122
4.6.
і
Monotonically Increasing Functions
...........................................................122
4.6.2
Monotonically Decreasing Functions
..........................................................124
4.6.3
Nonmonotonic Functions
............................................................................125
4.7
Characteristic Functions
...................................................................................130
4.8
Probability-Generating Functions
.....................................................................136
4.9
Moment-Generating Functions
.........................................................................139
4.10
Evaluating Tail Probabilities
..........................................................................140
4.11
Engineering Application
—
Scalar Quantization
.............................................148
4.12
Engineering Application
—
Entropy and Source Coding
................................155
Exercises
.........................................................................................................159
MATLAB
Exercises
........................................................................................174
Chapter
5;
Pairs of Random Variables
.............................................................. 177
5.1
Joint Cumulative Distribution Functions
..........................................................178
5.2
Joint Probability Density Functions
................................,.................................180
5.3
Joint Probability Mass Functions
........................................................,.............186
5.4
Conditional Distribution, Density, and Mass Functions
...................................188
5.5
Expected Values Involving Pairs of Random Variables
...................................192
5.6
Independent Random Variables
........................................................................197
5.7
Jointly Gaussian Random Variables
.................................................................202
5.8
Joint Characteristic and Related Functions
.......................................................206
5.9
Transformations of Pairs of Random Variables
...............................................210
5.10
Complex Random Variables
...........................................................................219
5.11
Engineering Application: Mutual Mormation, Channel
Capacity, and Channel Coding
.......................................................................221
Exercises
.........................................................................................................227
MATLAB
Exercises
.......................................................„............................... 242
Otapter6: Multiple Random Variables
____.....___...............................«...........245
6.1
Joint and Conditional PMFs, CDFs, and PDFs
..................................,.............245
6.2
Expectations Involving Multiple Random Variables
...............................,........247
6.3
Gaussian Random Variables in Multiple Dimensions
......................................249
6.4 Transformatioßs
Involving Multiple Random Variables
..................................252
Contents
vìi
6.4.1 Linear
Transformations
................................................................................253
6.4.2
Quadratic Transformations of Gaussian Random Vectors
.........................257
6.4.3
Order Statistics
............................................................................................260
6.4.4
Coordinate Systems in Three Dimensions
..................................................262
6.5
Estimation and Detection
...................................................................................264
6.5.1
Maximum a Posteriori Estimation
..............................................................265
6.5.2
Maximum Likelihood Estimation
...............................................................267
6.5.3
Minimum Mean Square Error Estimation
...................................................268
6.6
Engineering Application: Linear Prediction of Speech
.....................................272
Exercises
............................................................................................................277
MATLAB
Exercises
...........................................................................................287
Chapter
7:
Random Sums and Sequences
..........................................................289
7.1
Independent and Identically Distributed Random Variables
.............................289
7.1.1
Estimating the Mean of IID Random Variables
..........................................290
7.1.2
Estimating the Variance of IID Random Variables
....................................295
7.1.3
Estimating the CDF of IID Random Variables
...........................................297
7.2
Convergence Modes of Random Sequences
.....................................................298
7.2.1
Convergence Everywhere
...........................................................................300
7.2.2
Convergence Almost Every where
..............................................................301
7.2.3
Convergence in Probability
.........................................................................301
7.2.4
Convergence is the Mean Square Sense
......................................................302
7.2.5
Convergence in Distribution
.......................................................................302
7.3
The Law of Large Numbers
...............................................................................304
7.4
The Central Limit Theorem
...............................................................................306
7.5
Confidence Intervals
..........................................................................................310
7.6
Random Sums of Random Variables
.................................................................315
7.7
Engineering Application: A Radar System
.......................................................317
Exercises
............................................................................................................325
MATLAB
Exercises
...........................................................................................334
ChapterS: Random Processes
..........................................................................335
8.1
Definition and Classification of Processes
........................................................335
8.2
Mathematical Tools for Studying Random Processes
.......................................340
8.3
Stationary and Ergodic Random Processes
.......................................................348
8.4
Properties of the Autocorrelation Function
.......................................................356
8.5
Gaussian Random Processes
.............................................................................357
8.6
Poisson
Processes
..............................................................................................360
8.7
Engineering Application
—
Shot Noise in
ар
-η
Junction Diode
.......................365
Exercises
............................................................................................................371
MATLAB
Exercises
...........................................................................................381
Chapter
9:
Markov Processes
.......................................................................... 383
9.1
Definition and Examples of Markov Processes
.................................................383
9.2
Calculating Transition and State Probabilities in Markov Chains
....................388
9.3
Characterizatioa of Markov Chains
..................................................................,394
9.4
Continuous Time Markov Processes
...........................................,.....................401
9.5
Engineering Application: A Computer Communication Network
....................413
viii Contents
9.6 Engineering Application:
A
Telephone Exchange ...........................................416
Exercises
...........................................................................................................419
MATLAB
Exercises..........................................................................................
427
Chapter
10:
Power Spectral Density
.................................................................429
10.1
Definition of PSD
...........................................................................................430
10.2
The Wiener-Khintchine-Einstein Theorem
...................................................433
10.3
Bandwidth of a Random Process
....................................................................439
10.4
Spectral Estimation
.........................................................................................441
10.4.1
Non-parametric Spectral Estimation
.........................................................441
10.4.2
Parametric Spectral Estimation
.................................................................448
10.5
Thermal Noise
.................................................................................................452
10.6
Engineering Application: PSDs of Digital Modulation Formats
....................455
Exercises
.........................................................................................................463
MATLAB
Exercises
........................................................................................469
Chapter
11:
Random Processes in Linear Systems
..............................................473
11.1
Continuous Time Linear Systems
...................................................................473
11.2
Discrete-Time Linear Systems
........................................................................477
11.3
Noise Equivalent Bandwidth
..........................................................................479
11.4
Signal-to-Noise Ratios
....................................................................................480
11.5
The Matched Filter
..........................................................................................482
11.6
The Wiener Filter
............................................................................................486
11.7
Bandlimited and Narrowband Random Processes
..........................................494
11.8
Complex Envelopes
........................................................................................499
11.9
Engineering Application: An Analog Communication System
......................500
Exercises
.........................................................................................................505
MATLAB
Exercises
........................................................................................514
Chapter
12:
Simulation Techniques
..................................................................517
12.1
Computer Generation of Random Variables
..................................................517
12.1.1
Binary Pseudorandom Number Generators
...............................................517
12.1.2
Nonbinary Pseudorandom Number Generators
.........................................521
12.1.3
Generation of Random Numbers from a Specified Distribution
...............523
12.1.4
Generation of Correlated Random Variables
............................................524
12.2
Generation of Random Processes
...................................................................525
12.2.1
Frequency Domain Approach
....................................................................525
12.2.2
Time Domain Approach
............................................................................529
12.2.3
Generation of Gaussian White Noise
........................................................533
12.3
Simulation of Rare Events
..............................................................................534
12.3.1
Monte Carlo Simulations
..............................................,............................535
12.3.2
Importance Sampling
.................................................................................537
12.4
Engineering Application: Simulation of a Coded Digital
Communication System
........,.........................................................................539
Exercises
.......................................................,..............„.......................,„.......543
MATLAB
Exercises
...........................,............................................................546
Contents ix
Appendices
A
Review
of Set Theory
...........................................................................................547
В
Review of Linear Algebra
.....................................................................................551
С
Review of Signals and Systems
...........................................................................559
D
Summary of Common Random Variables
...........................................................565
E
Mathematical Tables
............................................................................................577
F
Numerical Methods for Evaluating the Q-Function
.............................................587
Index
.............................................................................................................593
|
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| author | Miller, Scott L. Childers, Donald G. |
| author_facet | Miller, Scott L. Childers, Donald G. |
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| dewey-full | 621.382/20151 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
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| dewey-raw | 621.382/20151 |
| dewey-search | 621.382/20151 |
| dewey-sort | 3621.382 520151 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Informatik Elektrotechnik / Elektronik / Nachrichtentechnik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV040491584 |
| illustrated | Illustrated |
| indexdate | 2024-12-24T02:51:22Z |
| institution | BVB |
| isbn | 9780123869814 0123869811 |
| language | English |
| lccn | 2011053022 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025338565 |
| oclc_num | 794668964 |
| open_access_boolean | |
| owner | DE-473 DE-BY-UBG DE-B768 |
| owner_facet | DE-473 DE-BY-UBG DE-B768 |
| physical | xii, 611 p. ill. 25 cm |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | Elsevier Academic Press |
| record_format | marc |
| spellingShingle | Miller, Scott L. Childers, Donald G. Probability and random processes with applications to signal processing and communications Mathematik Signal processing Mathematics Probabilities Stochastic processes Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Sprachverarbeitung (DE-588)4116579-2 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| subject_GND | (DE-588)4079013-7 (DE-588)4116579-2 (DE-588)4057630-9 |
| title | Probability and random processes with applications to signal processing and communications |
| title_auth | Probability and random processes with applications to signal processing and communications |
| title_exact_search | Probability and random processes with applications to signal processing and communications |
| title_full | Probability and random processes with applications to signal processing and communications Scott L. Miller, Donald Childers |
| title_fullStr | Probability and random processes with applications to signal processing and communications Scott L. Miller, Donald Childers |
| title_full_unstemmed | Probability and random processes with applications to signal processing and communications Scott L. Miller, Donald Childers |
| title_short | Probability and random processes |
| title_sort | probability and random processes with applications to signal processing and communications |
| title_sub | with applications to signal processing and communications |
| topic | Mathematik Signal processing Mathematics Probabilities Stochastic processes Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Sprachverarbeitung (DE-588)4116579-2 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| topic_facet | Mathematik Signal processing Mathematics Probabilities Stochastic processes Wahrscheinlichkeitstheorie Sprachverarbeitung Stochastischer Prozess |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025338565&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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