digital foundation

　　This intuitive yet rigorous introduction derives the core results of digital communication from first principles. Theory, rather than industry standards, motivates the engineering approaches, and key results are stated with all the required assumptions. The book emphasizes the geometric view, opening with the inner product, the matched filter for its computation, Parseval's theorem, the sampling theorem as an orthonormal expansion, the isometry between passband signals and their baseband representation, and the spectral-efficiency optimality of quadrature amplitude modulation (QAM).

　　Subsequent chapters address noise, hypothesis testing, Gaussian stochastic processes, and the sufficiency of the matched filter outputs. Uniquely, there is a treatment of white noise without generalized functions, and of the power spectral density without artificial random jitters and random phases in the analysis of QAM. This systematic and insightful book, with over 300 exercises, is ideal for graduate courses in digital communication, and for anyone asking 'why' and not just 'how'.

PrefaceAcknowledgments
Ch 1. Some essential notation
Ch 2. Signals, integrals, and sets of measure zero
Ch 3. The inner product;
Ch 4. The space L2 of energy-limited signals
Ch 5. Convolutions and filters
Ch 6. The frequency response of filters and bandlimited signals
Ch 7. Passband signals and their representation
Ch 8. Complete orthonormal systems and the sampling theorem
Ch 9. Sampling real passband signals
Ch 10. Mapping bits to waveforms
Ch 11. Nyquist's criterion
Ch 12. Stochastic processes: definition
Ch 13. Stationary discrete-time stochastic processes
Ch 14. Energy and power in PAM
Ch 15. Operational power spectral density
Ch 16. Quadrature amplitude modulation
Ch 17. Complex random variables and processes
Ch 18. Energy, power, and PSD in QAM
Ch 19. The univariate Gaussian distribution
Ch 20. Binary hypothesis testing
Ch 21. Multi-hypothesis testing
Ch 22. Sufficient statistics
Ch 23. The multivariate Gaussian distribution
Ch 24. Complex Gaussians and circular symmetry
Ch 25. Continuous-time stochastic processes
Ch 26. Detection in white Gaussian noise
Ch 27. Noncoherent detection and nuisance parameters
Ch 28. Detecting PAM and QAM signals in white Gaussian noise
Ch 29. Linear binary block codes with antipodal signaling

Appendix: On the Fourier seriesBibliographyTheorems referenced by nameAbbreviationsList of symbolsIndex