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Some properties of the multidimensional complex cepstrum and their relationship to the stability of multidimensional systems

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Abstract

Conditions are obtained for the cepstrum of anl 1 sequence having arbitrary support on theM-dimensional lattice to exist also as anl 1 sequence with arbitrary support. These conditions are used to show that the cepstrum of a sequence with support on a half-space will, when it exists, also have support on the same half-space. This result is used, in turn, to describe the support of the cepstrum of a sequence with bounded support on a half-space. The relationship between the existence of the cepstrum and bounded-input, bounded-output (BIBO) stability for all three of these cases is considered. Finally, the derivatives of the inversion operator, the homomorphic transform operator, and its inverse are calculated. These results are also useful in the one-dimensional case.

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Authors and Affiliations

  1. Lawrence Livermore National Laboratory, University of California, P.O. Box 808, L-97, 94550, Livermore, California, USA

    D. M. Goodman

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  1. D. M. Goodman
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This work was performed under the auspices of the U.S. Department of Energy by the Lawrence Livermore National Laboratory under contract number W-7405-ENG-48.

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Goodman, D.M. Some properties of the multidimensional complex cepstrum and their relationship to the stability of multidimensional systems. Circuits Systems and Signal Process 6, 3–30 (1987). https://doi.org/10.1007/BF01599003

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  • DOI: https://doi.org/10.1007/BF01599003

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