Table of Contents
ISRN Signal Processing
Volume 2011, Article ID 421502, 6 pages
http://dx.doi.org/10.5402/2011/421502
Research Article

A Method for the Recovery of Gaps in General Analytic Signals

1School of Engineering, Ruppin Academic Center, Emek-Hefer 40250, Israel
2School of Electrical Engineering, Faculty of Engineering, Tel-Aviv University, Tel-Aviv 69978, Israel

Received 27 May 2011; Accepted 10 July 2011

Academic Editor: L. Senhadji

Copyright © 2011 Benjamin G. Salomon and Hanoch Ur. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. G. G. Lorentz, Approximation of Functions, Chelsea, New York, NY, USA, 2nd edition, 1986.
  2. I. Sadka and H. Ur, “On Cadzow's non-iterative extrapolation of BL signals,” Signal Processing, vol. 59, no. 3, pp. 313–320, 1997. View at Google Scholar · View at Scopus
  3. A. Papoulis, “A new algorithm in spectral analysis and band-limited extrapolation,” IEEE Transactions on Circuits and Systems, vol. 22, pp. 735–742, 1975. View at Google Scholar
  4. R. W. Gerchberg, “Super-resolution through error energy reduction,” Optica Acta, vol. 21, pp. 709–720, 1974. View at Google Scholar
  5. R. P. Boas, Entire Functions, Academic Press, New York, NY, USA, 1954.
  6. J. C. Mason and D. C. Handscomb, Chebyshev Polynomials, Chapman Hall CRC, Boca Raton, Fla, USA, 2003.
  7. P. Corr, D. Stewart, P. Hanna, J. Ming, and F. J. Smith, “Discrete Chebyshev transform—a matural modification of the DCT,” in Proceedings of the 15th International Conference on Pattern Recognition (ICPR '00), vol. 3, pp. 1142–1145, Barcelona, Spain, 2000.
  8. V. E. Neagoe, “Chebyshev nonuniform sampling cascaded with the discrete cosine transform for optimum interpolation,” IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 38, no. 10, pp. 1812–1815, 1990. View at Publisher · View at Google Scholar · View at Scopus
  9. Z. D. Wang, G. A. Jullien, and W. C. Miller, “On computing Chebyshev optimal nonuniform interpolation,” Signal Processing, vol. 51, no. 3, pp. 223–228, 1996. View at Publisher · View at Google Scholar · View at Scopus
  10. N. Ahmed, T. Natarajan, and K. R. Rao, “Discrete cosine transform,” IEEE Transactions on Computers, vol. 23, pp. 90–93, 1974. View at Google Scholar
  11. V. Britanak, P. C. Yip, and K. R. Rao, Discrete Cosine and Sine Transforms: General Properties, Fast Algorithms and Integer Approximations, Academic Press, Amsterdam, The Netherlands, 2007.
  12. J. von Neumann, Functional Operators Vol. II: The Geometry of Orthogonal Spaces, Annals of Mathematics Studies no. 22, Princeton University Press, Princeton, NJ, USA, 1950, This is a reprint of mimeographed lecture notes first distributed in 1933.
  13. L. Debnath and P. Mikusinski, Introduction to Hilbert Spaces with Applications, Academic Press, New York, NY, USA, 2nd edition, 1998.
  14. H. Stark and Y. Yang, Vector Space Projections, John Willey & Sons, New York, NY, USA, 1998.
  15. D. C. Youla, “Generalized image reconstruction by the method of alternating orthogonal projections,” IEEE Transactions on Circuits and Systems, vol. 25, pp. 694–702, 1978. View at Google Scholar
  16. M. Goldburg and R. J. Marks, “Signal synthesis in the presence of an inconsistent set of constraints,” IEEE Transactions on Circuits and Systems, vol. 32, no. 7, pp. 647–663, 1985. View at Google Scholar · View at Scopus
  17. D. C. Youla and V. Velasco, “Extensions of a result on the synthesis of signals in the presence of inconsistent constraints,” IEEE Transactions on Circuits and Systems, vol. 33, no. 4, pp. 465–468, 1986. View at Google Scholar · View at Scopus
  18. L. Fox and I. B. Parker, Chebyshev Polynomials in Numerical Analysis, Oxford University Press, London, UK, 1968.
  19. J. L. Wu and J. Shiu, “Discrete cosine transform in error control coding,” IEEE Transactions on Communications, vol. 43, pp. 1857–1861, 1995. View at Google Scholar
  20. P. J. S. G. Ferreira, “Iterative and noniterative recovery of missing samples for 1-D band-limited signals,” in Nonuniform Sampling: Theory and Practice, F. Marvasti, Ed., pp. 235–278, Kluwer Academic/Plenum, New York, NY, USA, 2001. View at Google Scholar
  21. G. H. Golub and C. F. Van Loan, Matrix Computations, John Hopkins University Press, Baltimore, Md, USA, 3rd edition, 1996.
  22. X. G. Xia, “An extrapolation for general analytic signals,” IEEE Transactions on Signal Processing, vol. 40, no. 9, pp. 2243–2249, 1992. View at Publisher · View at Google Scholar · View at Scopus