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
- References
Bibliography
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
- References
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- A Foundation in Digital Communication , pp. 858 - 863Publisher: Cambridge University PressPrint publication year: 2017
References
, and (2003): Sobolev Spaces. Elsevier B.V., Amsterdam, The Netherlands, second edn.
(1990): An Introduction to Continuity, Extrema, and Related Topics for General Gaussian Processes. Institute of Mathematical Statistics, Hayward, CA.
(2015): Linear Algebra Done Right. Springer-Verlag New York, Inc., New York, third edn.
, , and (2004): Digital Communication. Springer-Verlag New York, Inc., New York, third edn.
(2005): Dynamic Programming and Optimal Control, vol. 1. Athena Scientific, Nashua, NH, third edn.
(1995): Probability and Measure. John Wiley & Sons, Inc., New York, third edn.
, and (1982): “A Bayes but not classically sufficient statistic,” The Annals of Statistics, 10(3), 1025–1026.Google Scholar
(2003): Algebraic Codes for Data Transmission. Cambridge University Press, New York.
Jr. (1954): Entire Functions. Academic Press Inc., New York.
(1998): Gaussian Measures. American Mathematical Society, Providence, RI.
(2007): Measure Theory: Volume I. Springer-Verlag, Berlin, Germany.
(1995): The Normal Distribution: Characterizations with Applications. Springer-Verlag New York, Inc., New York.
(2001): A Course in Probability Theory. Academic Press, San Diego, CA, third edn.
, , , and (2009): Introduction to Algorithms. The MIT Press, Cambridge, MA, third edn.
, and (2006): Elements of Information Theory. Wiley, Hoboken, NJ, second edn.
, and (2004): Stationary and Related Stochastic Processes: Sample Function Properties and Their Applications. Dover Publications, Inc., Mineola, NY.
Jr., and (1987): An Introduction to the Theory of Random Signals and Noise. IEEE Press, New York.
(1997): “A lower bound on the probability of a union,” Discrete Mathematics, 169, 217–220.Google Scholar
(1990): Stochastic Processes. John Wiley & Sons, Inc., New York.
(2003): Real Analysis and Probability. Cambridge University Press, New York, second edn.
, and (1972): Fourier Series and Integrals. Academic Press, Inc., San Diego.
(1988): Linear Least Squares Computations. Marcel Dekker, Inc., New York.
(1971): An Introduction to Probability Theory and Its Applications, vol. II. John Wiley & Sons, Inc., New York, second edn.
, and (1997): “Log-concavity and inequalities for chisquare, F and beta distributions with applications in multiple comparisons,” Statistica Sinica, 7(3), 771–787.Google Scholar
Jr. (1991): “Geometrically uniform codes,” IEEE Transactions on Information Theory, 37(5), 1241–1260.Google Scholar
(2008): Principles of Digital Communication. Cambridge University Press, New York.
, and (1996): Introduction to the Theory of Random Processes. Dover Publications, Inc., Mineola, NY.
, and (1996): Matrix Computations. The John Hopkins University Press, Baltimore, MD, third edn.
(2006): “Toeplitz and circulant matrices: a review,” Foundations and Trends in Communications and Information Theory, 2(3), 155–239.Google Scholar
, and (2001): Probability and Random Processes. Oxford University Press, New York, third edn.
(1950): Measure Theory. D. Van Nostrand Company, Inc., Princeton, NJ.
(1958): Finite-Dimensional Vector Spaces. D. Van Nostrand Company, Inc., Princeton, NJ.
, and (1949): “Application of the Radon-Nikodym theorem to the theory of sufficient statistics,” The Annals of Mathematical Statistics, 20(2), 225–241.Google Scholar
(1995): Elements of Signal Detection and Estimation. Prentice Hall, Englewood Cliffs, NJ.
(1975): Topics in Algebra. John Wiley & Sons, Inc., New York, second edn.
, and (2013): Matrix Analysis. Cambridge University Press, New York, second edn.
, and (1972): Distributions in Statistics: Continuous Multivariate Distributions. John Wiley & Sons, Inc., New York.
, , and (1994): Continuous Univariate Distributions, vol. 1. John Wiley & Sons, Inc., New York, second edn.
, , and (1995): Continuous Univariate Distributions, vol. 2. John Wiley & Sons, Inc., New York, second edn.
, , and B. Hassibi (2000): Linear Estimation. Prentice Hall, Inc., Upper Saddle River, NJ.
(2002): Foundations of Modern Probability. Springer, New York, second edn.
, and (1991): Brownian Motion and Stochastic Calculus. Springer-Verlag New York, Inc., New York, second edn.
, and (1966): Tchebycheff Systems: With Applications in Analysis and Statistics. John Wiley & Sons, Inc., New York.
(2004): An Introduction to Harmonic Analysis. Cambridge University Press, New York, NY, third edn.
(1988): Fourier Analysis. Cambridge University Press, New York, NY.
, and R. Sivan (1991): Modern Signals and Systems. Prentice Hall, Inc., Englewood Cliffs, NJ.
, and (2005): Testing Statistical Hypotheses. Springer-Verlag New York, Inc., New York, third edn.
(1991): “Signal sets matched to groups,” IEEE Transactions on Information Theory, 37(6), 1675–1682.Google Scholar
(1963): Probability Theory. D. Van Nostrand Company, Inc., Princeton, NJ, third edn.
Jr. (1978): “Theory of analytic modulation systems,” The Bell System Technical Journal, 57(3), 491–576.Google Scholar
, and (1977): The Theory of Error- Correcting Codes. North-Holland, Amsterdam, The Netherlands.
, , and (2011): Inequalities: Theory of Majorization and Its Applications. Springer, New York, NY, second edn.
(1975): Conformal Mapping. Dover Publications, Inc., Mineola, NY.
(1968): Processus Aléatoires Gaussiens. Les Presses de l'Université de Montréal.
, and (1997): Signals & Systems. Prentice Hall, Inc., Upper Saddle River, NJ, second edn.
(2002): Introduction to Fourier Analysis and Wavelets. Brooks/Cole, Pacific Grove, CA.
(1994): An Introduction to Signal Detection and Estimation. Springer-Verlag New York, Inc., New York, second edn.
(2008): Digital Processing of Random Signals: Theory and Methods. Dover Publications, Inc., Mineola, NY.
(2001): Foundations of Time Series Analysis and Prediction Theory. John Wiley & Sons, Inc., New York.
, and (2007): Digital Communications. McGraw-Hill Education, 5th edn.
(1980): “The zeros of entire functions: theory and engineering applications,” Proceedings of the IEEE, 68(3), 308–328.Google Scholar
, and (2008): Modern Coding Theory. Cambridge University Press, New York.
, and (1990): Functional Analysis. Dover Publications, Inc., Mineola, NY.
, and (1986): Counterexamples in Probability and Statistics. Chapman & Hall, New York.
(2005): “An elementary proof of Lyapunov's theorem,” The American Mathematical Monthly, 112(7), 651–653.Google Scholar
(2006): Introduction to Coding Theory. Cambridge University Press, New York.
, and (2010): Real Analysis. Prentice Hall, Inc., Upper Saddle River, NJ, fourth edn.
(1962): Fourier Analysis on Groups. John Wiley & Sons, New York.
(1976): Principles of Mathematical Analysis. McGraw-Hill, Inc., New York, third edn.
(1987): Real & Complex Analysis. McGraw-Hill, Inc., New York, third edn.
, and (2009): Channel Codes: Classical and Modern. Cambridge University Press.
, and (2006): “Performance analysis of linear codes under maximum-likelihood decoding: a tutorial,” Foundations and Trends in Communications and Information Theory, 3(1/2), 1–225.Google Scholar
(1996): Probability. Springer-Verlag New York, Inc., New York, second edn.
(2005): Orthogonal Polynomials on the Unit Circle. Part 1: Classical Theory. American Mathematical Society, Providence RI.
(2002): Probability Distributions Involving Gaussian Random Variables: A Handbook for Engineers and Scientists. Kluwer Academic Publishers, Norwell, MA.
, and (1961): “Prolate spheroidal wave functions, Fourier analysis and uncertainty—I,” The Bell System Technical Journal, 40(1), 43–63.Google Scholar
(2004): The Cauchy-Schwarz Master Class: An Introduction to the Art of Mathematical Inequalities. Cambridge University Press, New York.
, and (1971): Introduction to Fourier Analysis on Euclidean Spaces. Princeton University Press, Princeton, NJ.
(1990): The Multivariate Normal Distribution. Springer-Verlag New York, Inc., New York.
(1998): Introduction to Coding Theory. Springer-Verlag New York, Inc., New York, third edn.
(1998): Multiuser Detection. Cambridge University Press, New York.
, and (1979): Principles of Digital Communication and Coding. McGraw-Hill, Inc., New York.
(1991): Probability with Martingales. Cambridge University Press, New York.
(1986): Correlation Theory of Stationary and Related Random Functions: Volume I: Basic Results. Springer-Verlag.
(2011): Matrix Theory: Basic Results and Techniques. Springer-Verlag New York, Inc., New York, second edn.
(1997): “Matrix integrals and map enumeration: an accessible introduction,” Mathematical and Computer Modelling, 26(8–10), 281–304.Google Scholar