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Applied Optics

Applied Optics


  • Vol. 22, Iss. 6 — Mar. 15, 1983
  • pp: 826–829

Large symmetric π transformations for Hadamard transforms

E. E. Fenimore  »View Author Affiliations

Applied Optics, Vol. 22, Issue 6, pp. 826-829 (1983)

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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 Sylvester-type 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

Original Manuscript: November 15, 1982
Published: March 15, 1983

E. E. Fenimore, "Large symmetric π transformations for Hadamard transforms," Appl. Opt. 22, 826-829 (1983)

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  1. N. J. A. Sloane, T. Fine, P. G. Phillips, M. Harwit, Appl. Opt. 8, 2103 (1969). [CrossRef] [PubMed]
  2. E. D. Nelson, M. L. Fredman, J. Opt. Soc. Am. 60, 1664 (1970). [CrossRef]
  3. M. O. Harwit, Appl. Opt. 10, 1415 (1971). [CrossRef] [PubMed]
  4. A. Rosencwaig, Opt. Commun. 7, 305 (1973). [CrossRef]
  5. S. Miyamoto, Space Sci. Instrum. 3, 473 (1977).
  6. M. O. Harwit, N. J. A. Sloane, Hadamard Transform Optics (Academic, New York, 1979).
  7. J. Gunson, “A Fast Colvolution Transform for M-Sequences,” preprint, U. Birmingham, U.K. (1980).
  8. E. J. Watson, Math. Comput. 16, 368 (1962).
  9. E. E. Fenimore, G. S. Weston, Appl. Opt. 20, 3058 (1981). [CrossRef] [PubMed]
  10. E. E. Fenimore, T. M. Cannon, Appl. Opt. 17, 337 (1978). [CrossRef] [PubMed]

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