A novel derivation of the Agarwal-Cooley fast cyclic convolution algorithm based on the Good-Thomas Prime Factor algorithm

The Agarwal-Cooley fast cyclic convolution algorithm and the Good-Thomas Prime Factor algorithm have been traditionally independently derived. In this work we show how the Prime Factor Algorithm triggers the Agarwal-Cooley decomposition in the discrete time domain. A new polynomial expression based on the tensor product formulation of the Prime Factor Algorithm is used in conjunction with the cyclic convolution theorem, to obtain a novel and insightful derivation of the Agarwal-Cooley fast cyclic convolution algorithm