Fast DFT matrices transform based on generalized prime factor algorithm

Inspired by fast Jacket transforms, we propose simple factorization and construction algorithms for the M -dimensional discrete Fourier transform (DFT) matrices underlying generalized Chinese remainder theorem (CRT) index mappings. Based on successive coprime-order DFT matrices with respect to the CRT with recursive relations, the proposed algorithms are presented with simplicity and clarity on the basis of the yielded sparse matrices. The results indicate that our algorithms compare favorably with the direct-computation approach.