Two-dimensional periodically shift variant digital filters

Abstract

Two-dimensional (2-D) periodically shift variant (PSV) digital filters are considered. These filters have potential applications in processing video signals with cyclostationary noise, scrambling of digital images, and in 2-D multirate signal processing. The filters are formulated in the form of the Fornasini-Marchesini (FM) state-space model with periodic coefficients. This PSV model is then represented as a new shift-invariant system which is named the "Kiok-Neon" model. This model has several advantages that include ease of analysis and reduced computations compared to the existing state-space models. An algorithm is developed that transforms any given 2-D PSV FM system to its equivalent "Kiok-Neon" model. Invertibility of this model is an important consideration, especially in image scrambling applications. A condition is established for the invertibility of the "Kiok-Neon" model of the 2-D PSV system. Also, the inverse system can be easily computed from the original. It is established that the 2-D PSV system is asymptotically stable if an equivalent shift-invariant FM system is asymptotically stable. The established results are illustrated with examples.