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Analysis of 2-D state-space periodically shift-variant discrete systems

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Abstract

Two-dimensional (2-D) periodically shift-variant (PSV) digital filters are considered. These filters have applications in processing video signals with cyclostationary noise, scrambling digital images, and 2-D multirate signal processing. The filters are formulated in the form of a Givone-Roesser (GR) state-space model with periodic coefficients. This PSV model is then presented in block form as a shift-invariant system that also has the same GR state-space form. This block form has reduced computations and ease of analysis. An algorithm is developed that transforms any given 2-D PSV GR system to its equivalent shift-invariant model. Invertibility of this model is an important consideration, especially in image scrambling applications. A condition is established for the invertibility of the shift-invariant model of the 2-D PSV system. Also, the inverse system can be easily computed from the original. The established results are illustrated with an example.

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Authors and Affiliations

  1. Department of Electrical Engineering, University of Colorado, 80217-3364, Denver, Colorado

    Sreeraman Rajan, Kyung Sub Joo & Tamal Bose

Authors
  1. Sreeraman Rajan
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  2. Kyung Sub Joo
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  3. Tamal Bose
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This work was supported in part by a grant from the Colorado Advanced Software Institute.

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Rajan, S., Joo, K.S. & Bose, T. Analysis of 2-D state-space periodically shift-variant discrete systems. Circuits Systems and Signal Process 15, 395–413 (1996). https://doi.org/10.1007/BF01182594

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  • DOI: https://doi.org/10.1007/BF01182594

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