OSA's Digital Library

Applied Optics

Applied 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)

View Full Text Article

Enhanced HTML    Acrobat PDF (327 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



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

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

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)

Sort:  Author  |  Year  |  Journal  |  Reset  


  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]
  3. C. Saloma, “Computational complexity and the observation of physical signals,” J. Appl. Phys. 74, 5314–5319 (1993). [CrossRef]
  4. C. Saloma, M. Escobido, “Detection accuracy in zero-crossing-based spectrum analysis and image reconstruction,” Appl. Opt. 33, 7617–7621 (1994). [CrossRef] [PubMed]
  5. S. Howard, “Method for continuing Fourier spectra given by the fast Fourier transform,” J. Opt. Soc. Am. A 71, 1 (1981).
  6. P. Jansson, ed., Deconvolution with Applications to Spectroscopy (Academic, Tokyo, 1984), p. 261.
  7. A. Montowski, A. Stark, Introduction to Higher Algebra (Pergamon, Oxford, England, 1964), p. 364.
  8. R. Bracewell, The Fourier Transform and its Applications (Prentice-Hall, Englewood Cliffs, New Jersey, 1988), p. 104.
  9. J. Proakis, D. Manolakis, Digital Signal Processing: Principles, Algorithm, and Applications, 2nd ed. (Macmillan, New York, 1992), pp. 943–944.
  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]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


Fig. 1 Fig. 2 Fig. 3
Fig. 4

« Previous Article

OSA is a member of CrossRef.

CrossCheck Deposited