The ?eld of multirate signal processing has witnessed a great deal of progress and an increasingly wide range of applications since the publication of the ?rst textbook by Crochiere and Rabiner (1983). However this progress has been mainly in the area of deterministic systems with emphasis on perfe- reconstruction and/or orthogonal systems. This book introduces a statistical theory for extracting information from signals that have di?erent sampling rates. This new theory generalizes the conventional (deterministic) theory of multirate systems beyond many of its constraints.Furthermore itallowsfortheformulationofseveralnewproblems such as spectrum estimation time-delay estimation and sensor fusion in the realm of multirate signal processing. I have arrived at the theory presented here by integrating concepts from diverse areas such as information theory inverse problems and theory of - equalities. The process of merging a variety of concepts of di?erent origin results in both merits and shortcomings. The former include the fresh and - di?erentiated view of an amateur providing scope of application. The latter include a lack of in-depth experience in each of the original ?elds. Granted this may lead to gaps in continuity however it goes without saying that a complete theory can seldom be achieved by one person and in a short time. My goal in writing this book has been to inspire the reader to initiate his own research and add to the theory of multirate statistical signal processing