In April 1965 American mathematician James W. Cooley of IBM Watson Research Center, Yorktown Heights, New York, and American statistician John W. Tukey published "An algorithm for the machine calculation of complex Fourier series", Mathematics of Computation 19, 297–301. This paper enunciated the Cooley-Tukey FFT algorithm, the most common fast Fourier transform algorithm.
"The motivation for it [FFT algorithm] was provided by Dr. Richard L. Garwin at IBM Watson Research who was concerned about verifying a Nuclear arms treaty with the Soviet Union for the SALT talks. Garwin thought that if he had a very much faster Fourier Transform he could plant sensors in the ground in countries surrounding the Soviet Union. He suggested the idea of how Fourier transforms could be programmed to be much faster to both Cooley and Tukey. They did the work, the sensors were planted, and he was able to locate nuclear explosions to within 15 kilometers of where they were occurring" (Wikipedia article on James Cooley, accessed 03-06-2012).