Book contents
- Frontmatter
- Dedication
- Contents
- Preface to the Second Edition
- Preface to the First Edition
- Acknowledgments for the Second Edition
- Acknowledgments for the First Edition
- 1 Some Essential Notation
- 2 Signals, Integrals, and Sets of Measure Zero
- 3 The Inner Product
- 4 The Space L2 of Energy-Limited Signals
- 5 Convolutions and Filters
- 6 The Frequency Response of Filters and Bandlimited Signals
- 7 Passband Signals and Their Representation
- 8 Complete Orthonormal Systems and the Sampling Theorem
- 9 Sampling Real Passband Signals
- 10 Mapping Bits to Waveforms
- 11 Nyquist's Criterion
- 12 Stochastic Processes: Definition
- 13 Stationary Discrete-Time Stochastic Processes
- 14 Energy and Power in PAM
- 15 Operational Power Spectral Density
- 16 Quadrature Amplitude Modulation
- 17 Complex Random Variables and Processes
- 18 Energy, Power, and PSD in QAM
- 19 The Univariate Gaussian Distribution
- 20 Binary Hypothesis Testing
- 21 Multi-Hypothesis Testing
- 22 Sufficient Statistics
- 23 The Multivariate Gaussian Distribution
- 24 Complex Gaussians and Circular Symmetry
- 25 Continuous-Time Stochastic Processes
- 26 Detection in White Gaussian Noise
- 27 Noncoherent Detection and Nuisance Parameters
- 28 Detecting PAM and QAM Signals in White Gaussian Noise
- 29 Linear Binary Block Codes with Antipodal Signaling
- 30 The Radar Problem
- 31 A Glimpse at Discrete-Time Signal Processing
- 32 Intersymbol Interference
- A On the Fourier Series
- B On the Discrete-Time Fourier Transform
- C Positive Definite Functions
- D The Baseband Representation of Passband Stochastic Processes
- Bibliography
- Theorems Referenced by Name
- Abbreviations
- List of Symbols
- Index
19 - The Univariate Gaussian Distribution
Published online by Cambridge University Press: 02 March 2017
Book contents
- Frontmatter
- Dedication
- Contents
- Preface to the Second Edition
- Preface to the First Edition
- Acknowledgments for the Second Edition
- Acknowledgments for the First Edition
- 1 Some Essential Notation
- 2 Signals, Integrals, and Sets of Measure Zero
- 3 The Inner Product
- 4 The Space L2 of Energy-Limited Signals
- 5 Convolutions and Filters
- 6 The Frequency Response of Filters and Bandlimited Signals
- 7 Passband Signals and Their Representation
- 8 Complete Orthonormal Systems and the Sampling Theorem
- 9 Sampling Real Passband Signals
- 10 Mapping Bits to Waveforms
- 11 Nyquist's Criterion
- 12 Stochastic Processes: Definition
- 13 Stationary Discrete-Time Stochastic Processes
- 14 Energy and Power in PAM
- 15 Operational Power Spectral Density
- 16 Quadrature Amplitude Modulation
- 17 Complex Random Variables and Processes
- 18 Energy, Power, and PSD in QAM
- 19 The Univariate Gaussian Distribution
- 20 Binary Hypothesis Testing
- 21 Multi-Hypothesis Testing
- 22 Sufficient Statistics
- 23 The Multivariate Gaussian Distribution
- 24 Complex Gaussians and Circular Symmetry
- 25 Continuous-Time Stochastic Processes
- 26 Detection in White Gaussian Noise
- 27 Noncoherent Detection and Nuisance Parameters
- 28 Detecting PAM and QAM Signals in White Gaussian Noise
- 29 Linear Binary Block Codes with Antipodal Signaling
- 30 The Radar Problem
- 31 A Glimpse at Discrete-Time Signal Processing
- 32 Intersymbol Interference
- A On the Fourier Series
- B On the Discrete-Time Fourier Transform
- C Positive Definite Functions
- D The Baseband Representation of Passband Stochastic Processes
- Bibliography
- Theorems Referenced by Name
- Abbreviations
- List of Symbols
- Index
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- A Foundation in Digital Communication , pp. 373 - 394Publisher: Cambridge University PressPrint publication year: 2017