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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.