Radix-K FFT´s using K-point convolutions

A new class of DFT algorithms, so-called C-FFTs, is presented. The radix-K C-FFTs are derived from structures composed of K-point convolutions and K-point DFTs. Radix-3, 4, and 6 C-FFTs have the smallest arithmetical complexities, and in contrast to other existing algorithms, this fact does not depend on the complex number base used. Additionally, the transformation of C-FFTs into algorithms for real-valued data is straightforward. The analysis of radix-6 C-FFTs leads to a refinement of the "split-radix" FFT concept. The refinement can be used for deriving improved radix-K FFTs when K is a product of mutually prime numbers.