A modified discrete fourier transform algorithm: A delta rotation algorithm

A new method for the evaluation of the Discrete Fourier Transform (DFT) is presented. This method evaluates the DFT of samples of a continuous time signal by multiplying the DFT of the difference signal at the output of a Linear Delta Modulator (LDM) by a rotation factor. The novelty of the proposed algorithm is to reduce the number of multiplication and to simplify the hardware implementation. Further modification of this algorithm does not require any multiplication at all during the DFT computation. An implementation of convolutions, chirp-z transform and the discrete Hilbert transform with the proposed technique will offer good opportunities for additional research with respect to the point of a simple hardware implementation, high-speed, and a computational simplicity. This proposed technique is, in fact, the combination of an encoding technique and a FFT algorithm. The results show a very promising and will be a viable alternative to the FFT and any other DFT algorithms.