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Many signal and image processing applications impose a severe demand on the I/O bandwidth and computation power of general-purpose computers. The "systolic" concept offers guidelines in building cost-effective systems that balance I/O with computation. The resulting simplicity and regularity of such systems leads to modular designs suitable for VLSI implementation. We describe here a linear systolic array capable of evaluating a large class of inner-product functions used in signal and image processing. These include matrix multiplication, multidimensional convolutions using fixed or time-varying kernels, as well as various nonlinear functions of vectors. The system organization of a working prototype is also described.