On computing the fast Fourier transform
Communications of the ACM
Implementing Clenshaw-Curtis quadrature, II computing the cosine transformation
Communications of the ACM
On Computing the Discrete Cosine Transform
IEEE Transactions on Computers
A register transfer module FFT processor for speech analysis
AFIPS '72 (Fall, part II) Proceedings of the December 5-7, 1972, fall joint computer conference, part II
Algebraic signal processing theory: Cooley-Tukey type algorithms for real DFTs
IEEE Transactions on Signal Processing
A procedure for implementing the fast Fourier transform on small computers
IBM Journal of Research and Development
A microprocessor for signal processing, the RSP
IBM Journal of Research and Development
FFT algorithms for vector computers
Parallel Computing
An efficient DMT modem for the G.LITE ADSL transceiver
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
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A new procedure is presented for calculating the complex, discrete Fourier transform of real-valued time series. This procedure is described for an example where the number of points in the series is an integral power of two. This algorithm preserves the order and symmetry of the Cooley-Tukey fast Fourier transform algorithm while effecting the two-to-one reduction in computation and storage which can be achieved when the series is real. Also discussed are hardware and software implementations of the algorithm which perform only (N/4) log2 (N/2) complex multiply and add operations, and which require only N real storage locations in analyzing each N-point record.