State Space Methods In Multidimensional Digital Signal Processing

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State Space Methods in Multidimensional Digital Signal Processing

This report summarizes the results of an extensive research program on the real-time implementation of multidimensional (M-D) digital signal processing algorithms. We began our study on the efficient implementation of M-D digital filters. We mapped the M-D digital filter to a state space model because the state space model supports local data communications. We studied various approaches to implementing the state space model for M-D digital signal processing applications. We found that the best approach involves mapping the state space model onto a generalized linear finite state machine which facilitates the hardware implementation. Using this approach, we were able to develop a multiprocessor system architecture which is scalable, which is modular, and which has a high efficiency. Based upon these results, we developed the architecture for an application specific computing system which we call a Block Data Flow Architecture (BDFA). We are currently studying the mapping of several other M-D signal processing algorithms and matrix operations to the BDFA. These studies show that multiprocessor systems using the BDFA can achieve high throughput and high efficiency at a modest cost.
Multidimensional Systems: Signal Processing and Modeling Techniques

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Multidimensional Signals and Systems

This book covers the theory of multidimensional signals and systems and related practical aspects. It extends the properties and mathematical tools of one-dimensional signals and systems to multiple dimensions and covers relevant timeless topics including multidimensional transformations, multidimensional sampling as well as discrete multidimensional systems. A special emphasis is placed on physical systems described by partial differential equations, the construction of suitable integral transformations and the implementation of the corresponding discrete-time algorithms. To this end, signal spaces and functional transformations are introduced at a mathematical level provided by undergraduate programs in engineering and science. The presentation takes a comprehensive, illustrative and educational approach without reference to a particular application field. Instead, the book builds a solid theoretical concept of multidimensional signals and systems and shows the application to various problems relevant for practical scenarios.