A Review Of Signal Processing With Systolic Arrays

This paper reviews recent developments in signal processing and surveys recent progress in parallel processing algorithms and architectures for their real-time implementation. It has previously been shown1-2 that the major computational requirements for many important real-time signal processing tasks can be reduced to a common set of basic matrix operations including matrix-vector multiplication, matrix-matrix multiplication and addition, matrix inversion, solution of systems of linear equations, least squares approximate solution of linear systems, eigensystem solution, generalized eigen-systems solution, and singular value decomposition (SVD) of matrices. To this list, we would now add the generalized singular value decompositions of Van Loan3,4 and Paige-Saunders5. The first five matrix operations listed above may be computed non-iteratively, and systolic array architectures and algorithms are available which provide modular parallelism, local interconnects, regular data flow, and high efficiency, with the efficiency essentially constant as the parallelism is increased6-8. Parallel computation of eigensystems, generalized eigensystems, the singular value decomposition, and the generalized singular value decomposition is more difficult, since the computation is necessarily iterative, and it is difficult to utilize only local communication between processing elements while maintaining high efficiency. Algorithms for the latter problems are therefore still the subject of intensive research.

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