OPTIMAL MEASUREMENT TECHNIQUES UTILIZING HADAMARD TRANSFORMS

A classic measurement problem-weighing n objects on a scale of limited absolute accuracy-is addressed, with a modern application of this pro blem-Hadamard-transform spectroscopy. For both of these measurement sy stems, optimal recovery of the desired measurements requires computati on of a Hadamard transform. With the advent of digital-signal-processi ng methods, researchers soon realized that this transform could be per formed most efficiently with a fast-Hadamard-transform (FHT) algorithm . However, in addition to introducing greater speed into these measure ment systems, the FHT introduced some confusion because there are seve ral different orderings or equivalence classes of Hadamard matrices an d FHT's that could be used. The goal of this paper is to relieve the c onfusion about the applicability of existing techniques for dealing wi th ordering problems by 1) clarifying under what conditions these tech niques work, 2) explaining under what conditions they fail and why, an d 3) presenting a new technique (requiring less memory and fewer compu tational steps) that never fails.