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

Sreeraman Rajan, Kyung Sub Joo, Tamal Bose

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)395-413
Number of pages19
JournalCircuits, Systems, and Signal Processing
Issue number3
StatePublished - 1996

ASJC Scopus subject areas

  • Signal Processing
  • Applied Mathematics


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