Three‐dimensional Fourier convolution with an array processor Free

This paper describes techniques for reducing CPU time, memory, and I/O time required to perform a three‐dimensional convolution on real data, and the use of an array processor. These techniques capitalize on the Hermitian nature of the Fourier transform of mathematically real input data, take advantage of convolution kernels having mirror symmetry in three dimensions, and eliminate trivial transformations. The result is convolution over a three‐dimensional 64×64×64 array containing 250 K real elements that requires only 28 s to execute. Memory space of a medium‐sized array processor is sufficiently large for the procedures to be carried out on entire real, single‐precision arrays at one time without transferring data between the array processor and disk storage.