Probability, random variables, and random signal principles:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | Undetermined |
| Published: |
Boston, Mass. [u.a.]
McGraw-Hill
2001
|
| Edition: | 4. ed. |
| Series: | McGraw-Hill series in electrical and computer engineering
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVIII, 462 S. graph. Darst. |
| ISBN: | 0071181814 9780071181815 |
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MARC
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| 100 | 1 | |a Peebles, Peyton Z. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Probability, random variables, and random signal principles |c Peyton Z. Peebles |
| 250 | |a 4. ed. | ||
| 264 | 1 | |a Boston, Mass. [u.a.] |b McGraw-Hill |c 2001 | |
| 300 | |a XVIII, 462 S. |b graph. Darst. | ||
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Record in the Search Index
| _version_ | 1804138755562405888 |
|---|---|
| adam_text | CONTENTS
Preface
XVII
Probability
1
1.0
Introduction to Book and Chapter
1
1.1
Set Definitions
3
1.2
Set Operations
4
Venn Diagram
/
Equality and Difference
/
Union and
Intersection
j
Complement
/
Algebra of Sets
/ De
Morgan s
Laws
/
Duality Principle
1.3
Probability Introduced through Sets and Relative
Frequency
9
Experiments and Sample Spaces
/
Discrete and Continuous
Sample Spaces
/
Events
/
Probability Definition and Axioms
/
Mathematical Model of Experiments
/
Probability as a Relative
Frequency
1.4
Joint and Conditional Probability
14
Joint Probability
/
Conditional Probability
j
Total
Probability
¡
Bayes
Theorem
1.5
Independent Events
20
Two Events I Multiple Events
/
Properties of Independent
Events
1.6
Combined Experiments
24
Combined Sample Space
/
Events on the Combined Space
/
Probabilities
/
Permutations
/
Combinations
1.7
Bernoulli Trials
28
1.8
Summary
31
Problems
32
The Random Variable
41
2.0
Introduction
41
2.1
The Random Variable Concept
41
Definition of a Random Variable
/
Conditions for a Function to
Be a Random Variable
/
Discrete and Continuous Random
Variables
/
Mixed Random Variable
2.2
Distribution Function
44
2.3
Density Function
47
Existence I Properties of Density Functions
2.4
The Gaussian Random Variable
51
ix
2.5
Other Distribution and Density Examples
54
Binomial
/
Poisson
/
Uniform
/
Exponential
/
Rayleigh
2.6
Conditional Distribution and Density Functions
60
Conditional Distribution
/
Properties of Conditional
Distribution I Conditional Density
/
Properties of Conditional
Density I
*
Methods of Defining Conditioning Event
2.7
Summary
66
Problems
66
Operations on One Random Variable
-
Expectation
77
3.0
Introduction
77
3.1
Expectation
77
Expected Value of a Random Variable
/
Expected Value of a
Function of a Random Variable
/ *
Conditional Expected Value
3.2
Moments
81
Moments about the Origin
/
Central Moments
/
Variance and
Skew
j
Chebychev s Inequality
j
Markov s Inequality
*3.3 Functions That Give Moments
84
*
Characteristic Function
/
Moment Generating Function
/
Chernoff s Inequality and Bound
3.4
Transformations of a Random Variable
87
Monotonie
Transformations of a Continuous Random
Variable
/
Nonmonotonic Transformations of a Continuous
Random Variable
/
Transformation of a Discrete Random
Variable
3.5
Computer Generation of One Random Variable
93
3.6
Summary
96
Problems
97
Multiple Random Variables
107
4.0
Introduction
107
4.1
Vector Random Variables
108
4.2
Joint Distribution and Its Properties
109
Joint Distribution Function
/
Properties of the Joint
Distribution I Marginal Distribution Functions
4.3
Joint Density and Its Properties
113
Joint Density Function
/
Properties of the Joint Density
/
Marginal Density Functions
4.4
Conditional Distribution and Density
116
Conditional Distribution and Density
-
Point Conditioning
/
*
Conditional Distribution and Density
-
Interval Conditioning
4.5
Statistical Independence
121
4.6
Distribution and Density of a Sum of Random
Variables
122
Sum of Two Random Variables
/
Sum of Several Random
Variables
*4.7 Central Limit Theorem
125
*
Unequal Distribution
/ *
Equal Distributions
4.8
Summary
129
Problems
129
Operations on Multiple Random Variables
141
5.0
Introduction
141
5.1
Expected Value of a Function of Random Variables
141
Joint Moments about the Origin
/
Joint Central Moments
*5.2 Joint Characteristic Functions
146
5.3
Jointly Gaussian Random Variables
148
Two Random Variables
/
*N Random Variables
j
*Some
Properties of Gaussian Random Variables
*5.4 Transformations of Multiple Random Variables
153
*One Function
j
*
Multiple Functions
*5.5 Linear Transformation of Gaussian Random
Variables
157
*5.6 Computer Generation of Multiple Random Variables
159
5.7
Sampling and Some Limit Theorems
163
Sampling and Estimation
/
Estimation of Mean, Power, and
Variance
/
Weak Law of Large Numbers
/
Strong Law of
Large Numbers
*5.8 Complex Random Variables
168
5.9
Summary
169
Problems
169
Random Processes
-
Temporal Characteristics
179
6.0
Introduction
179
6.1
The Random Process Concept
179
Classification of Processes
/
Deterministic and Nondeterministic
Processes
6.2
Staţionari
ty
and Independence
185
Distribution and Density Functions
/
Statistical Independence
/
First-Order Stationary Processes
/
Second-Order and Wide-
Sense Stationarity
/
N-Order and Strict-Sense Stationarity
/
Time Averages and Ergodicity
/
Mean-Ergodic Processes
/
Correlation-Ergodic Processes
6.3
Correlation Functions
194
Autocorrelation Function and Its Properties
/
Cross-Correlation
Function and Its Properties
/
Covariance Functions
/
Discrete-
Time Processes and Sequences
6.4
Measurement of Correlation Functions
200
6.5
Gaussian Random Processes
201
6.6
Poisson
Random Process
203
Probability Density Function
/
Joint Probability Density
*6.7 Complex Random Processes
206
6.8
Summary
208
Problems
208
7
Random Processes
-
Spectral Characteristic
220
7.0
Introduction
220
7.1
Power Density Spectrum and Its Properties
220
The Power Density Spectrum
/
Properties of the Power Density
Spectrum I Bandwidth of the Power Density Spectrum
7.2
Relationship between Power Spectrum and
Autocorrelation Function
227
7.3
Cross-Power Density Spectrum and Its Properties
230
The Cross-Power Density Spectrum
/
Properties of the Cross-
Power Density Spectrum
*7.4 Relationship between Cross-Power Spectrum and
Cross-Correlation Function
234
7.5
Power
Spectrums
for Discrete-Time Processes and
Sequences
237
Discrete-Time Processes
/
Discrete-Time Sequences
/
Discrete
Fourier Transform
7.6
Some Noise Definitions and Other Topics
246
White and Colored Noise
/
Product Device Response to a
Random Signal
*7.7 Power
Spectrums
of Complex Processes
254
7.8
Summary
255
Problems
256
8
Linear Systems with Random Inputs
270
8.0
Introduction
270
8.1
Linear System Fundamentals
270
The General Linear System
/
Linear Time-Invariant Systems
/
Time-Invariant System Transfer Function
/
Idealized Systems
/
Causal and Stable Systems
8.2
Random Signal Response of Linear Systems
276
System Response
—
Convolution
/
Mean and Mean-Squared
Value of System Response
/
Autocorrelation Function of
Response I Cross-Correlation Functions of Input and Output
8.3
System Evaluation Using Random Noise
279
8.4
Spectral Characteristics of System Response
280
Power Density Spectrum of Response
/
Cross-Power Density
Spectrums
of Input and Output
/
Measurement of Power
Density
Spectrums
8.5
Noise
Bandwidth
8.6
Bandpass, Band-Limited, and Narrowband Processes
Band-Limited Processes
/
Narrowband Processes
/
Properties of
Band-Limited Processes
/ *
Proof of Properties of Band-Limited
Processes
8.7
Sampling of Processes
Baseband Sampling Theorem
/
Baseband Sampling Theorem for
Random Processes
/
Bandpass Sampling of Random
Processes I Discrete-Time Power
Spectrums
8.8
Discrete-Time Systems
A/D Conversion
/ D/A
Conversion
/
The Discrete-Time
System
f
Sequence Domain Methods for DT Systems
/
Transform Domain Methods for DT Systems
8.9
Modeling of Noise Sources
Resistive (Thermal) Noise Source
/
Arbitrary Noise Sources,
Effective Noise Temperature
/
An Antenna as a Noise Source
8.10
Incremental Modeling of Noisy Networks
Available Power Gain
/
Equivalent Networks, Effective Input
Noise Temperature
/
Spot Noise Figures
8.11
Modeling of Practical Noisy Networks
Average Noise Figures
/
Average Noise Temperatures
/
Modeling of Attenuators
/
Model of Example System
8.12
Summary
Problems
9
Optimum Linear Systems
9.0
Introduction
9.1
Systems That Maximize Signal-to-Noise Ratio
Matched Filter for Colored Noise
/
Matched Filter for White
Noise
9.2
Systems That Minimize Mean-Squared Error
Wiener Filters
/
Minimum Mean-Squared Error
9.3
Optimization by Parameter Selection
9.4
Summary
Problems
10
Some Practical Applications of the Theory
10.0
Introduction
10.1
Noise in an Amplitude Modulation Communication
System
AM System and Waveforms
/
Noise Performance
10.2
Noise in a Frequency Modulation Communication
System
FM
System and Waveforms
/ FM
System Performance
10.3
Noise in a Simple
Control
System
386
Transfer Function
/
Error Function
/
Wiener Filter Application
10.4
Noise in a Phase-Locked Loop
389
Phase Detector
/
Loop Transfer Function
/
Loop Noise
Performance
10.5
Characteristics of Random Computer-Type
Waveform
396
Process Description
/
Power Spectrum
/
Autocorrelation
Function
10.6
Envelope and Phase of a Sinusoidal Signal plus Noise
398
Waveforms
/
Probability Density of the Envelope
/
Probability
Density of Phase
10.7
Radar Detection Using a Single Observation
401
False Alarm Probability and Threshold
/
Detection Probability
10.8
Summary
405
Problems
406
Appendix A Review of the Impulse Function
412
Basic Review
412
Other Forms of Impulses
414
Properties of Impulses
414
Definition I Derivatives
/
Linearity
/
Fourier Transforms of
Impulses
j
Fourier Transforms of Derivatives of Impulses
j
Shifting I Product of a Function and Impulse
/
Product of a
Function and Derivative of Impulse
/
Convolution of Two
Impulses
Appendix
В
Gaussian Distribution Function
417
Appendix
С
Useful Mathematical Quantities
419
Trigonometric Identities
419
Indefinite Integrals
420
Rational Algebraic Functions
/
Trigonometric Functions
/
Exponential Functions
Definite Integrals
422
Finite Series
423
Infinite Series
423
Appendix
D
Review of Fourier Transforms
424
Existence
425
Properties
425
Linearity I Time and Frequency Shifting
/
Scaling
/
Duality
/
Differentiation
/
Integration
/
Conjugation
/
Convolution
/
Correlation
f
Parseval s Theorem
Multidimensional
Fourier
Transforms
427
Problems
428
Appendix
E
Table of Useful Fourier Transforms
433
Appendix
F
Some Probability Densities and
Distributions
435
Discrete Functions
436
Bernoulli I Binomial
/
Pascal
/
Poisson
Continuous Functions
438
Arcsine I Beta
/
Cauchy
/
Chi-Square with
N
Degrees of
Freedom
j
Erlang /
Exponential
/
Gamma
/
Gaussian-
Univariate
/
Gaussian-Bivariate
/
Laplace
/
Log-Normal
/
Rayleigh I Rice
/
Uniform
/
Weibull
Appendix
G
Some Mathematical Topics of Interest
444
Leibniz s Rule
444
Interchange of Derivative and Integral
445
Interchange of Integrals
445
Continuity of Random Processes
445
Differentiation of Random Processes
446
Integration of Random Processes
446
Interchange of Expectation and Integration
447
Holder s Inequality
448
Schwarz
s
Inequality
449
Minkowski s Inequality
449
Bibliography
450
Index
453
|
| any_adam_object | 1 |
| author | Peebles, Peyton Z. |
| author_facet | Peebles, Peyton Z. |
| author_role | aut |
| author_sort | Peebles, Peyton Z. |
| author_variant | p z p pz pzp |
| building | Verbundindex |
| bvnumber | BV023646298 |
| classification_rvk | ZN 6025 |
| ctrlnum | (OCoLC)247254009 (DE-599)BVBBV023646298 |
| dewey-full | 519.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 |
| dewey-search | 519.2 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Elektrotechnik / Elektronik / Nachrichtentechnik |
| edition | 4. ed. |
| format | Book |
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| id | DE-604.BV023646298 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:33:14Z |
| institution | BVB |
| isbn | 0071181814 9780071181815 |
| language | Undetermined |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017242644 |
| oclc_num | 247254009 |
| open_access_boolean | |
| owner | DE-523 DE-859 DE-739 |
| owner_facet | DE-523 DE-859 DE-739 |
| physical | XVIII, 462 S. graph. Darst. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | McGraw-Hill |
| record_format | marc |
| series2 | McGraw-Hill series in electrical and computer engineering |
| spelling | Peebles, Peyton Z. Verfasser aut Probability, random variables, and random signal principles Peyton Z. Peebles 4. ed. Boston, Mass. [u.a.] McGraw-Hill 2001 XVIII, 462 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier McGraw-Hill series in electrical and computer engineering Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Zufallsvariable (DE-588)4129514-6 gnd rswk-swf Stochastisches Signal (DE-588)4140374-5 gnd rswk-swf Stochastisches Signal (DE-588)4140374-5 s DE-604 Zufallsvariable (DE-588)4129514-6 s 1\p DE-604 Wahrscheinlichkeitstheorie (DE-588)4079013-7 s 2\p DE-604 Stochastischer Prozess (DE-588)4057630-9 s 3\p DE-604 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017242644&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Peebles, Peyton Z. Probability, random variables, and random signal principles Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Zufallsvariable (DE-588)4129514-6 gnd Stochastisches Signal (DE-588)4140374-5 gnd |
| subject_GND | (DE-588)4079013-7 (DE-588)4057630-9 (DE-588)4129514-6 (DE-588)4140374-5 |
| title | Probability, random variables, and random signal principles |
| title_auth | Probability, random variables, and random signal principles |
| title_exact_search | Probability, random variables, and random signal principles |
| title_full | Probability, random variables, and random signal principles Peyton Z. Peebles |
| title_fullStr | Probability, random variables, and random signal principles Peyton Z. Peebles |
| title_full_unstemmed | Probability, random variables, and random signal principles Peyton Z. Peebles |
| title_short | Probability, random variables, and random signal principles |
| title_sort | probability random variables and random signal principles |
| topic | Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Zufallsvariable (DE-588)4129514-6 gnd Stochastisches Signal (DE-588)4140374-5 gnd |
| topic_facet | Wahrscheinlichkeitstheorie Stochastischer Prozess Zufallsvariable Stochastisches Signal |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017242644&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT peeblespeytonz probabilityrandomvariablesandrandomsignalprinciples |