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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 35, Iss. 32 — Nov. 10, 1996
  • pp: 6417–6422

Spectral recovery by analytic continuation in crossing-based spectrum analysis

Carlo Mar Blanca, Vincent Ricardo Daria, and Caesar Saloma  »View Author Affiliations


Applied Optics, Vol. 35, Issue 32, pp. 6417-6422 (1996)
http://dx.doi.org/10.1364/AO.35.006417


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Abstract

By the use of analytic continuation, the correct spectrum of an undersampled analog input signal fa (t) of a true bandwidth B is recovered from an aliased Fourier spectrum that is computed directly from a data set consisting of sinusoid-crossing locations {ti }, where the signal fa (t) intersects with a reference sinusoid r(t) with a frequency of W < B/2 and an amplitude of A. If A ≥ |fa (t)| within the sampling period T, then a crossing exists within each time interval Δ = 1/2W, and a total of 2WT = 2M sinusoid crossings are detected, where M is a positive integer. The cut-off frequency for sampling is W = ±M/T. In a crossing detector, a trade-off exists between the size of Δ and the accuracy with which a crossing can be located within it because the detector has a finite response time. Low-accuracy detection of the crossing positions degrades the detection limit of the detector and results in a computed Fourier spectrum that contains spurious wideband frequencies. We show however that, if fa (t) has a known compact support within T, then sampling at a frequency of W < B/2 may still be possible because the correct fa (t) spectrum can be recovered from the aliased spectrum by means of analytic continuation. The technique is demonstrated for an interferogram test signal in both the absence and presence of additive Gaussian noise.

© 1996 Optical Society of America

History
Original Manuscript: September 11, 1995
Revised Manuscript: June 3, 1996
Published: November 10, 1996

Citation
Carlo Mar Blanca, Vincent Ricardo Daria, and Caesar Saloma, "Spectral recovery by analytic continuation in crossing-based spectrum analysis," Appl. Opt. 35, 6417-6422 (1996)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-35-32-6417


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References

  1. C. Saloma, V. Daria, “Performance of a zero-crossing optical spectrum analyzer,” Opt. Lett. 18, 1468–1470 (1993). [CrossRef] [PubMed]
  2. C. Saloma, P. Haeberli, “Optical spectrum analysis from zero crossings,” Opt. Lett. 16, 1535–1537 (1991). [CrossRef] [PubMed]
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  10. W. Press, W. Vetterling, S. Teukolsky, B. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, New York, 1992), pp. 41–43.
  11. C. Saloma, “Reconstructing the Hartley intensity spectrum from its sinusoidal crossings,” Opt. Lett. 20, 1–3 (1995). [CrossRef] [PubMed]
  12. C. Saloma, “Wavelet transform analysis directly from sinusoid crossings,” Phys. Rev. E 53, 1962–1966 (1996). [CrossRef]

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