Many multiplexing instruments utilize the fast Hadamard transform (FHT) to demultiplex the signal. In the past, the FHT includes the π1 and π2 transformations to reorder vectors before and after a Sylvestertype Hadamard transform. Although the computational effort involved in the π1 and the Sylvester-type Hadamard transform scales as n log2n, calculating the π2 transformation (which only has to be done once) scales as n2. Recently Gunson (1980) has suggested a method by which the π transformations are symmetric, that is π2 = π1. We have calculated a complete set of symmetric π transformations for FHT of sizes 23 to 230. Special emphasis has been placed on the phase of the π transformation so as to have the correct phase in the demultiplexed signal.
© 1983 Optical Society of America
E. E. Fenimore, "Large symmetric π transformations for Hadamard transforms," Appl. Opt. 22, 826-829 (1983)