Systolic FFT algorithms on Boolean cube networks

A description is given of a systolic Cooley-Tukey fast Fourier transform algorithm for Boolean n-cubes with a substantial amount of storage per cube node. In mapping a Cooley-Tukey type FFT to such a network, the main concerns are effective use of the high connectivity/bandwidth of the Boolean n-cube, the computational resources, the storage bandwidth, if there is a storage hierarchy, and the pipelines should the arithmetic units have such a feature. Another important consideration in a multiprocessor, distributed storage architecture is the allocation and access to coefficients, if they are precomputed. FFT algorithms are described that use both the storage bandwidth and the communication system optimally and require storage of P+nN coefficients for a transform on P⩾ N data elements. A complex-to-complex FFT on 16 million points is predicted to require about 1.5 s on a Connection Machine model CM-2