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Two recently developed ideas, the conversion of a discrete Fourier transform (DFT) to convolution and the implementation of short convolutions with a minimum of multiplications, are combined to give efficient algorithms for long transforms. Three transform algorithms are compared in terms of the number of multiplications and additions. Timing for a prime factor fast Fourier transform (FFT) algorithm using high-speed convolution, which was programmed for an IBM 370 and an 8080 microprocessor, is presented.
Kolba et al. (Mon,) studied this question.
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