Frequency-Domain Separable Decomposition of 2-Dimensional Systems

  • N. M. Mitrou
  • G. I. Stassinopoulos
  • E. N. Protonotarious
Part of the Applied Information Technology book series (AITE)


Fan filters in seismic data processing, directional filters in image processing and 2-D equalizers are but a few examples of 2-Dimensional systems described explicitly in the frequency domain. Current methods for handling such systems in a discrete form require an NxN sampling grid resulting in considerable design complexity and a high implementation cost.

The approach presented here consists of approximating a desired 2-Dimensional response function through decomposing it into a sum of L separable terms. The advantages gained by such a decomposition are the following:
  1. 1.

    The analysis and design problem is reduced to a 1-D one.

  2. 2.

    Application of parallel-processing techniques is allowed.

  3. 3.

    The number of elements required for the implementation is now 2xLxN; in the case where L << N, appreciable simplification and economy is obtained.


Applications are given through design examples of 2-D low-pass, fan and Wiener filtering.


Impulse Response Singular Value Decomposition Frequency Response Function Wiener Filter Effective Domain 


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  1. [1]
    J. Allen, Computer architecture for digital signal processing, Proc. IEEE, No. 5, vol. 73, pp. 852–73, (May, 1985).CrossRefGoogle Scholar
  2. [2]
    P.R. Cappello and K. Steiglitz, Completely-pipelining architectures for digital signal processing, IEEE Trans. Accoust., Speech and Signal Processing, No. 4, vol. 31, pp. 1016–23, (Aug. 1983).CrossRefGoogle Scholar
  3. [3]
    D.E. Dudgeon and R.M. Mersereau, Multidimensional digital signal processing, Prentice-Hall, Englewood Cliffs, New Jersey, (1984).Google Scholar
  4. [4]
    S. Treitel and J.L. Shanks, The design of multistage separable planar filters, IEEE Trans. Geos. Electron., No. 1, vol. 9, pp. 10–27, (Jan. 1971).CrossRefGoogle Scholar
  5. [5]
    N. Dunford and J.T. Schwartz, Linear operators, John Wiley, New York, (1963).MATHGoogle Scholar
  6. [6]
    G.F. Roach, Green’s functions, 2nd Ed., Cambridge University Press, Cambridge, (1982).MATHGoogle Scholar
  7. [7]
    S. Treitel, J.L. Shanks and C.W. Frasier, Some aspects on fan filtering, Geophysics, vol. 32, pp. 789–800, (Oct. 1967).CrossRefGoogle Scholar
  8. [8]
    K.L. Peacock, On the practical design of discrete velocity filters for seismic data processing, IEEE Trans Accoust., Speech and Signal Processing, No. 1, vol. 30, pp. 52–60, (Feb. 1982).CrossRefGoogle Scholar
  9. [9]
    M. Kunt, A. Ikonomopoulos and M. Kocher, Second-generation image-coding techniques, Proc. IEEE, No. 4, vol. 73, pp. 549–574, (Apr. 1985).CrossRefGoogle Scholar
  10. [10]
    G. Strang, Linear algebra and its applications, 2nd Ed., Academic Press, New York, (1980).Google Scholar

Copyright information

© Plenum Press, New York 1986

Authors and Affiliations

  • N. M. Mitrou
    • 1
  • G. I. Stassinopoulos
    • 2
  • E. N. Protonotarious
    • 2
  1. 1.Department of ElectronicsNuclear Research Center „Democritos“AttikiGreece
  2. 2.Division of Computer ScienceNational Technical University of AthensGreece

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