A combing method of cocyclic DFT matrices by the Chinese remainder theorem

Abstract

Employing Chinese remainder theorem (CRT) index mapping for DFT matrices, a notation referred as cocyclic DFT matrices is proposed. Following the mathematical proof, it can be seen that using CRT index scheme proves the resulting DFT matrix in possession of cocyclic property. By exploiting the close relationship of successively lower order DFT matrices, a fast construction approach for general cocyclic DFT matrices is described in simple way. The proposed construction algorithm is presented for simplicity and clarity for it only minimally related to sparse matrices. The result indicates the presented fast algorithm performs quite well at decreasing the computation complexity.