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

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