An algorithm to compute unified complex Hadamard transform

Abstract

This paper focuses on the study of unified complex Hadamard transforms (UCHT) whose transformation matrices contain elements /spl plusmn/1 and /spl plusmn/i. New properties of the UCHT are presented. From the newly discovered properties, the UCHT is conveniently calculated by computing real Walsh Hadamard transform (WHT) of real and imaginary parts of a set of data, which are multiplied by a set of constant complex values, and multiplying the transformed values by some constant complex factors.