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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 71, Iss. 7 — Jul. 1, 1981
  • pp: 819–824

Continuation of discrete Fourier spectra using a minimum-negativity constraint

Samuel J. Howard  »View Author Affiliations

JOSA, Vol. 71, Issue 7, pp. 819-824 (1981)

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A method for continuing Fourier spectra applicable to spectra given by the discrete Fourier transform is presented. From the principle of minimizing the sum of the square of the negative values of the restored function, a set of simultaneous nonlinear equations is obtained. The only means of solution at present is iterative, but computational time is comparable with that for noniterative methods. Excellent restoration is obtained for the sharply attenuated spectrum of deconvolved infared peaks. The numerical procedure developed here lends itself easily to the inclusion of additional constraints to enhance resolution further. The constraints of minimum negativity and finite extent may both be enforced together on pertinent data with only slight modification of the procedure.

© 1981 Optical Society of America

Samuel J. Howard, "Continuation of discrete Fourier spectra using a minimum-negativity constraint," J. Opt. Soc. Am. 71, 819-824 (1981)

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  1. S. J. Howard, "Method for continuing Fourier spectra given by the fast Fourier transform," J. Opt. Soc. Am. 71, 95–98 (1981).
  2. B. R. Frieden, in Picture Processing and Digital Filtering, T. S. Huang, ed. (Springer-Verlag, New York, 1975), Chap. 5.
  3. A. C. Schell, "Enhancing the angular resolution of incoherent sources," Radio Electron. Eng. 29, 21–26 (1965).
  4. Y. Biraud, "A new approach for increasing the resolving power by data processing," Astron. Astrophys. 1, 124–127 (1969).
  5. P. A. Jansson, R. H. Hunt, and E. K. Plyor, "Resolution enhancoment of spectra," J. Opt. Soc. Am. 60, 596–599 (1970).
  6. J. P. Burg, "Maximum entropy spectral analysis," presented at the 37th Annual Society of Exploration Geophysicists Meeting, Oklahoma City, Okla., 1967.
  7. F. B. Hildebrand, Introduction to Numerical Analysis (McGraw-Hill, New York, 1965), pp. 450–451.

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