An efficient algorithm for the conjugate symmetric sequency-ordered complex Hadamard transform

In this paper, an efficient algorithm for fast computation of the conjugate symmetric sequency-ordered complex Hadamard transform (CS-SCHT) of any length that is a power of two is proposed using the Kronecker product. Since the CS-SCHT matrix is factored into a product of sparse matrices, the resulting structure for the algorithm is very attractive for implementation and similar to that of the well-known Walsh-Hadamard transform, except for some multiplications by -1 or (-√(-1)). It is shown that the proposed N-point complex-valued CS-SCHT algorithm requires Nlog₂(N) complex additions/subtractions and (N/2-1) multiplications by (-√(-1)).