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On the Use of Fast Hadamard Transforms for Spectrum Recovery in Hadamard Transform Spectroscopy

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The spectrum-recovery step in Hadamard transform spectroscopy is commonly implemented with a fast Hadamard transform (FHT). When the Hadamard or simplex matrix corresponding to the mask does not have the same ordering as the Hadamard matrix corresponding to the FHT, a modification is required. When the two Hadamard matrices are in the same equivalence class, this modification can be implemented as a permutation scheme. This paper investigates permutation schemes for this application. The investigation clarifies inaccurate claims about the applicability of existing methods; reveals a new, more efficient method; and leads to an extension that allows a permutation scheme to be applied to any Hadamard or simplex matrix in the appropriate equivalence class.

Keywords: Dispersive spectroscopy; Hadamard transform spectrometry; Multiplex spectrometry; Spectrum-recovery methods

Document Type: Research Article

DOI: http://dx.doi.org/10.1366/0003702924123700

Affiliations: Department of Electrical and Computer Engineering, Kansas State University, Manhattan, Kansas 66506

Publication date: September 1, 1992

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