Time series with mixed spectra - Li, Ta-Hsin (CRC Press, 2013)
"Preface This book focuses on the methods and theory for statistical analysis of time series with mixed spectra. A time series is said to have a mixed spectrum if it comprises a finite number of sinusoids with different frequencies plus random noise. The research on such time series has a long history, and it remains active to this day, especially in the signal processing community where the interest is driven in part by the everlasting desire for fast algorithms to reduce the computational cost. Despite of its importance, the subject often receives limited coverage in standard textbooks for understandable reasons. The objective of this book is to provide a more comprehensive and in-depth treatment of the subject. Needless to say, it is impossible to coverage every aspect of the subject, not only because of the huge literature which keeps growing to this day, but also due to the limited ability and capacity of the author. The topics in this book are selected to reflect what the author thinks are most interesting and relevant. The intended audience of the book includes graduate students, researchers, engineers, and other professionals who work in the fields of time series analysis and signal processing. In most part, the book only requires basic knowledge of probability, statistics, and time series analysis. Some theoretical results, especially their proofs, require more advanced knowledge of asymptotic analysis. For this reason, the proofs are deferred to the last section of each chapter in order not to interrupt the flow of intuitive interpretations which are more easily accessible to most readers. To serve the interests of a broader audience, the book deals with both real- and complex-valued time series"--