Properties and applications of unified complex Hadamard transforms

A family of Unified Complex Hadamard Transforms derived from Walsh functions is defined. Newly developed direct matrix operator is introduced which is able to generate different types of Complex Hadamard matrices. Higher dimension matrices of the transforms may also be generated recursively by means of Kronecker product from basic matrices. Sparse matrix factorization or matrix partitioning of the Complex Hadamard matrices leads to the fast algorithms with complexity Nlog₂N. One of the shown fast algorithms may be implemented as in-place architecture which reduces memory requirements and allows on simple implementation in software or in hardware. Finally, different properties of the new transforms are shown and the performance of the transforms for Wiener filtering is evaluated and compared with the known discrete orthogonal transforms