Book contents
- Frontmatter
- Contents
- Preface
- Acknowledgments
- 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
- A On the Fourier Series
- Bibliography
- Theorems Referenced by Name
- Abbreviations
- List of Symbols
- Index
Preface
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- Preface
- Acknowledgments
- 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
- A On the Fourier Series
- Bibliography
- Theorems Referenced by Name
- Abbreviations
- List of Symbols
- Index
Summary
Claude Shannon, the father of Information Theory, described the fundamental problem of point-to-point communications in his classic 1948 paper as “that of reproducing at one point either exactly or approximately a message selected at another point.” How engineers solve this problem is the subject of this book. But unlike Shannon's general problem, where the message can be an image, a sound clip, or a movie, here we restrict ourselves to bits. We thus envision that the original message is either a binary sequence to start with, or else that it was described using bits by a device outside our control and that our job is to reproduce the describing bits with high reliability. The issue of how images or text files are converted efficiently into bits is the subject of lossy and lossless data compression and is addressed in texts on information theory and on quantization.
The engineering solutions to the point-to-point communication problem greatly depend on the available resources and on the channel between the points. They typically bring together beautiful techniques from Fourier Analysis, Hilbert Spaces, Probability Theory, and Decision Theory. The purpose of this book is to introduce the reader to these techniques and to their interplay.
The book is intended for advanced undergraduates and beginning graduate students. The key prerequisites are basic courses in Calculus, Linear Algebra, and Probability Theory. A course in Linear Systems is a plus but not a must, because all the results from Linear Systems that are needed for this book are summarized in Chapters 5 and 6.
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- A Foundation in Digital Communication , pp. xvii - xxiiiPublisher: Cambridge University PressPrint publication year: 2009