Digital signal processing with complex Hadamard transform

The basic signal processing properties of the complex Hadamard transform are shown. Sparse matrix factorization or matrix partitioning of the complex Hadamard matrix leads to fast algorithms with complexity Nlog₂N. One of the fast algorithms shown may be implemented as an in-place architecture which reduces memory requirements and allows 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 are evaluated and compared with the known discrete orthogonal transforms