At about the 35 minute mark of this fascinating and witty talk by Paul Horowitz - one of the co-authors of “The Art of Electronics” there’s a short bit about the suitcase-portable SETI kit which uses a 68000 powered WICAT WS150 and a dual 68000 FFT appliance.
There was a WICAT still running in production in 2010.
Also in this talk some hints on the history of the FFT algorithm. Which led me to this paper
Cooley, J. W. (1987). The re-discovery of the fast Fourier transform algorithm. Mikrochimica Acta, 93(1-6), 33–45. doi:10.1007/bf01201681
Even with this nice inversion property, when the number of terms in the series and the number of x’s is N, the number of operations is N^2. The FFT algorithms which I am talking about here reduce this to N log(N), a speed-up of a factor of N/log (N). Modest sized sample records start at around N=1000 meaning a speed-up factor of 100. The spectrometry calculation I will mention later had N=512000 meaning that if one even considered the calculation by a direct method, the speed-up factor would be about 12800.
Howard Smith, a member of the APL group, put the algorithm in APL when it was only a language for defining processes and before it was implemented on any machine. This gave the algorithm a thorough working over at the other seminars.