Algorithms: Algorithm 338: algol procedures for the fast Fourier transform
By Richard C. Singleton
Communications of the ACM,
Vol. 11 No. 11, Pages 773-776
10.1145/364139.364167
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 log2n, where n is the number of data points.
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