A new FFT algorithm and its implementation on the DSP96002

A novel algorithm for computing the discrete Fourier transform (DFT) is presented. This fast Fourier transform (FFT) algorithm is obtained through decomposition of the Fourier matrix representing the DFT operator into a product of sparse matrices which are not all square matrices. The algorithm is based on additive properties of the input and output indexing sets of the Fourier transformation. Mathematical formulations of the algorithm are presented using tensor product algebra. Properties of this algebra are used to assist in the adaptation of the algorithm to the DSP96002 microprocessor architecture. This results in efficient implementations which take into account the inherent software and hardware features of the microprocessor.<>