Complex-valued random signals are embedded in the very fabric of science and engineering, yet the usual assumptions made about their statistical behavior are often a poor representation of the underlying physics. This book deals with improper and noncircular complex signals, which do not conform to classical assumptions, and it demonstrates how correct treatment of these signals can have significant payoffs. The book begins with detailed coverage of the fundamental theory and presents a variety of tools and algorithms for dealing with improper and noncircular signals. It provides a comprehensive account of the main applications, covering detection, estimation, and signal analysis of stationary, nonstationary, and cyclostationary processes. Providing a systematic development from the origin of complex signals to their probabilistic description makes the theory accessible to newcomers. This book is ideal for graduate students and researchers working with complex data in a range of research areas from communications to oceanography.
Peter J. Schreier is a Senior Lecturer in the School of Electrical Engineering and Computer Science, The University of Newcastle, Australia. He received his Ph.D. in electrical engineering from the University of Colorado at Boulder in 2003. He currently serves on the Editorial Board of the IEEE Transactions on Signal Processing, and on the IEEE Technical Committee of Machine Learning for Signal Processing.
Louis L. Scharf is Professor of Electrical and Computer Engineering and Statistics at Colorado State University. He received his Ph.D. from the University of Washington at Seattle in 1969. He has since received numerous awards for his research contributions to statistical signal processing, including an IEEE Distinguished Lectureship, an IEEE Third Millennium Medal, and the Technical Achievement and Society Awards from the IEEE Signal Processing Society. He is a Life Fellow of the IEEE.
1. The origins and uses of complex signals; 2. Introduction to complex random vectors and processes; 3. Second-order description of complex random vectors; 4. Correlation analysis; 5. Estimation; 6. Performance bounds for parameter estimation; 7. Detection; 8. Wide-sense stationary processes; 9. Nonstationary processes; 10. Cyclostationary processes; Appendix A. Rudiments of matrix analysis; Appendix B. Complex differential calculus (Wirtinger calculus); Appendix C. Introduction to majorization.