Optimal design of discrete coefficient DFTs for spectral analysis: extension to multiplierless FFTs

In a previous paper it has been shown that the complex coefficients of a discrete Fourier transform (DFT) used in spectral analysis, can be replaced by an optimum set whose real and imaginary components are constrained to be integer powers of two or the sum of two integer powers of two thus making multiplication trivial. However, the technique used ruled out any further increase in speed and reduction in hardware cost by factorisation of the DFT. The scheme presented in the paper overcomes this drawback and is applicable to the Cooley-Tukey fast Fourier transform algorithm.