Efficient method for recovering the optimal unbiased linear spectrum-estimate from Hadamard transform spectrometers having nonideal masks

T. W. Johnson, J. B. Park, S. A. Dyer, B. K. Harms, R. A. Dyer

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A spectrum-recovery method is presented which efficiently computes an optimal unbiased linear spectrum-estimate for measurements obtained with Hadamard transform (HT) spectrometers having nonideal masks. This method has the following advantages over other spectrum-recovery techniques: it is computationally efficient, it requires no additional measurements, and it computes an optimal spectrum-estimate. In the method presented, after the mask of the HT spectrometer has been characterized, approximately 3N preliminary arithmetic operations are performed once for a given spectrometer, where N is both the number of spectral resolution-elements desired and the number of measurements required. Each spectrum-estimate to be recovered then requires only an additional O[N(log2 + 4)] arithmetic operations. In contrast, conventional methods for obtaining an optimal unbiased linear spectrum-estimate require O(N3) preliminary operations, and O(2N2) operations during each spectrum-recovery.

Original languageEnglish
Pages (from-to)746-750
Number of pages5
JournalApplied Spectroscopy
Issue number5
Publication statusPublished - 1989 Jan 1


All Science Journal Classification (ASJC) codes

  • Instrumentation
  • Spectroscopy

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