Minimal realization and L2-sensitivity analysis for 3-D separable-denominator digital filters

The problems of minimal state-space realization for a three-dimensional (3-D) separable-denominator digital filter and analysis of l₂-sensitivity for the realized 3-D state-space model are investigated. First, a 3-D transfer function with separable denominator is expressed as a cascade connection of three one-dimensional (1-D) transfer functions by applying a minimal decomposition technique. Next, each 1-D transfer function is realized by a state-space model of minimal order. The l₂-sensitivity of a 3-D separable-denominator transfer function with respect to the state-space paramters is then analyzed based on a pure l₂ norm. Finally, a numerical example is presented to evaluate the l₂-sensitivity of a 3-D state-space model realized from a given 3-D separable-denominator digital filter.