Multirate Statistical Signal Processing

Multirate Statistical Signal Processing

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.

Theory of Multirate Statistical Signal Processing [microform]

Theory of Multirate Statistical Signal Processing and Applications

This dissertation develops basic theory and applications of statistical multirate signal processing. Specific tools and terminology for describing multirate systems in the time and frequency domains are presented. An optimal multirate estimator is derived in both a direct form and recursive form. The Recursive form of the optimal estimator allows calculation of the relative change in performance when input signals are added or removed from the multirate system. The optimal multirate filtering problem also is specialized to the case of optimal multirate linear prediction. An efficient method for calculating the multirate linear prediction coefficients and error variances is developed through the use of the multichannel Levinson recursion and generalized triangular UL factorization. Finally, a multirate sequential classifier is derived and applied to the problem of target classification. It is shown that classifier parameters needed for implementing the multirate sequential classifier are the same as those for multirate linear prediction. The methods presented in this dissertation are useful for multisensor fusion particularly when the sensors are operating at different rates.