An Introduction to the Theory of Random Signals and Noise

Cover Image Copyright Year: 1987
Author(s): Wilbur B. Davenport; William L. Root
Book Type: Wiley-IEEE Press
Content Type : Books
Topics: Signal Processing & Analysis
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Abstract

This "bible" of a whole generation of communications engineers was originally published in 1958. The focus is on the statistical theory underlying the study of signals and noises in communications systems, emphasizing techniques as well s results. End of chapter problems are provided.

Sponsored by:
IEEE Communications Society

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    Probability

    Copyright Year: 1987

    Wiley-IEEE Press eBook Chapters

    This chapter contains sections titled:

  • Introduction

  • Fundamentals

  • Joint Probabilities

  • Conditional Probabilities

  • Statistical Independence

  • Examples

  • Problems

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    Random Variables and Probability Distributions

    An Introduction to the Theory of Random Signals and Noise
    Copyright Year: 1987

    Wiley-IEEE Press eBook Chapters

    This chapter contains sections titled:

  • Definitions

  • Probability Distribution Functions

  • Discrete Random Variables

  • Continuous Random Variables

  • Statistically Independent Random Variables

  • Functions of Random Variables

  • Random Processes

  • Problems

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    Averages

    An Introduction to the Theory of Random Signals and Noise
    Copyright Year: 1987

    Wiley-IEEE Press eBook Chapters

    This chapter contains sections titled:

  • Statistical Averages

  • Moments

  • Characteristic Functions

  • Correlation

  • Correlation Functions

  • Convergence

  • Integrals of Random Processes

  • Time Averages

  • Problems

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    Sampling

    An Introduction to the Theory of Random Signals and Noise
    Copyright Year: 1987

    Wiley-IEEE Press eBook Chapters

    This chapter contains sections titled:

  • Introduction

  • The Sample Mean

  • Convergence of the Sample Mean

  • The Central Limit Theorem

  • Relative Frequency

  • Problems

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    Spectral Analysis

    An Introduction to the Theory of Random Signals and Noise
    Copyright Year: 1987

    Wiley-IEEE Press eBook Chapters

    This chapter contains sections titled:

  • Introduction

  • The Spectral Density of a Periodic Function

  • Spectral Density of a Periodic Random Process

  • Orthogonal Series Expansion of a Random Process

  • Spectral Density for an Arbitrary Function

  • Spectral Analysis of a Wide-sense Stationary Random Process

  • Cross-spectral Densities

  • Problems

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    Shot Noise

    An Introduction to the Theory of Random Signals and Noise
    Copyright Year: 1987

    Wiley-IEEE Press eBook Chapters

    This chapter contains sections titled:

  • Electronics Review

  • The Probability Distribution of Electron-emission Times

  • Average Current through a Temperature-limited Diode

  • Shot-noise Spectral Density for a Temperature-limited Diode

  • Shot-noise Probability Density for a Temperature-limited Diode

  • Space-charge Limiting of Diode Current

  • Shot Noise in a Space-charge-limited Diode

  • Shot Noise in Space-charge-limited Triodes and Pentodes

  • Problems

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    The Gaussian Process

    An Introduction to the Theory of Random Signals and Noise
    Page(s): 145 - 170
    Copyright Year: 1987

    Wiley-IEEE Press eBook Chapters

    This chapter contains sections titled:
    The Gaussian Random Variable
    The Bivariate Distribution
    The Multivariate Distribution
    The Gaussian Random Process
    The Narrow-band Gaussian Random Process
    Sine Wave Plus Narrow-band Gaussian Random Process
    Problems View full abstract»

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    Linear Systems

    An Introduction to the Theory of Random Signals and Noise
    Copyright Year: 1987

    Wiley-IEEE Press eBook Chapters

    This chapter contains sections titled:

  • Elements of Linear-system Analysis

  • Random Inputs

  • Output Correlation Functions and Spectra

  • Thermal Noise

  • Output Probability Distributions

  • Problems

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    Noise Figure

    An Introduction to the Theory of Random Signals and Noise
    Copyright Year: 1987

    Wiley-IEEE Press eBook Chapters

    This chapter contains sections titled:

  • Definitions

  • Noise Figure

  • Cascaded Stages

  • Example

  • Problems

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    Optimum Linear Systems

    An Introduction to the Theory of Random Signals and Noise
    Copyright Year: 1987

    Wiley-IEEE Press eBook Chapters

    This chapter contains sections titled:

  • Introduction

  • Smoothing and Predicting of Stationary Inputs Using the Infinite Past (Wiener Theory)

  • Pure Prediction: Nondeterministic Processes

  • Solution of the Equation for Predicting and Filtering

  • Other Filtering Problems Using Least-mean-square Error Criterion Phillips' Least-mean-square Error Filter

  • Smoothing and Predicting with a Finite Observation Time

  • Maximizing Signal-to-noise Ratio: The Matched Filtert

  • Problems

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    Nonlinear Devices: The Direct Method

    An Introduction to the Theory of Random Signals and Noise
    Copyright Year: 1987

    Wiley-IEEE Press eBook Chapters

    This chapter contains sections titled:

  • General Remarks

  • The Square-law Detector

  • The Square-law Detector: Signal-plus-Noise Input

  • The Half-wave Linear Detector

  • Problems

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    Nonlinear Devices: The Transform Method

    An Introduction to the Theory of Random Signals and Noise
    Copyright Year: 1987

    Wiley-IEEE Press eBook Chapters

    This chapter contains sections titled:

  • The Transfer Function

  • vth-Law Devices

  • The Output Autocorrelation Function, and Spectral Density

  • The Output Spectral Density

  • Narrow-band Inputs

  • vth-Law Detectors

  • Problems

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    Statistical Detection of Signals

    An Introduction to the Theory of Random Signals and Noise
    Copyright Year: 1987

    Wiley-IEEE Press eBook Chapters

    This chapter contains sections titled:

  • Application of Statistical Notions to Radio and Radar

  • Testing of Statistical Hypotheses

  • Likelihood Tests

  • Statistical Estimation

  • Communication with Fixed Signals in Gaussian Noise

  • Signals with Unknown Parameters in Gaussian Noise

  • Radar Signals in Gaussian Noise

  • Problems

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    Appendix 1: The Impulse Function

    An Introduction to the Theory of Random Signals and Noise
    Copyright Year: 1987

    Wiley-IEEE Press eBook Chapters

    This appendix contains sections titled:

  • Definitions

  • The Sifting Integral

  • Fourier Transforms

  • Derivatives of Impulse Functions

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    Appendix 2: Integral Equations

    An Introduction to the Theory of Random Signals and Noise
    Copyright Year: 1987

    Wiley-IEEE Press eBook Chapters

    This appendix contains sections titled:

  • Definitions

  • Theorems

  • Rational Spectra

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    Bibliography

    An Introduction to the Theory of Random Signals and Noise
    Page(s): 383 - 389
    Copyright Year: 1987

    Wiley-IEEE Press eBook Chapters

    This "bible" of a whole generation of communications engineers was originally published in 1958. The focus is on the statistical theory underlying the study of signals and noises in communications systems, emphasizing techniques as well s results. End of chapter problems are provided.

    Sponsored by:
    IEEE Communications Society View full abstract»

  • Full text access may be available. Click article title to sign in or learn about subscription options.

    Index

    An Introduction to the Theory of Random Signals and Noise
    Page(s): 391 - 393
    Copyright Year: 1987

    Wiley-IEEE Press eBook Chapters

    This "bible" of a whole generation of communications engineers was originally published in 1958. The focus is on the statistical theory underlying the study of signals and noises in communications systems, emphasizing techniques as well s results. End of chapter problems are provided.

    Sponsored by:
    IEEE Communications Society View full abstract»



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