Richard C. Singleton
Abstract
The following procedures are based on the Cooley-Tukey algorithm [1] for computing the finite Fourier transform of a complex data vector; the dimension of the data vector is assumed here to be a power of two. Procedure COMPLEXTRANSFORM computes either the complex Fourier transform or its inverse. Procedure REALTRANSFORM computes either the Fourier coefficients of a sequence of real data points or evaluates a Fourier series with given cosine and sine coefficients. The number of arithmetic operations for either procedure is proportional to n log2 n, where n is the number of data points.
- 1 COOLEY, J. W., and TUKEY, J. W. An algorithm for the machine calculation of complex Fourier series. Math. Comput. 19, 90, (Apr. 1965), 297-301.Google Scholar
Cross Ref
- 2 SINGLETON, R. C. On computing the fast Fourier transform. Comm. ACM 10 (Oct. 1967), 647-654. Google ScholarDigital Library
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