Realization of 3-D separable-denominator digital filters with very low l2-sensitivity

This paper investigates the problem of reducing the deviation from a desired transfer function caused by the coefficient quantization errors of a three-dimensional (3-D) separable-denominator digital filter. First, a 3-D transfer function with separable denominator is represented with the cascade connection of three one-dimensional (1-D) transfer functions by applying a minimal decomposition technique. Next, the multiinput multi-output (MIMO) 1-D transfer function located in the middle of the cascade connection is realized by a minimal state-space model and then the l₂/l₂-sensitivity of the model is analyzed. Third, a technique for the optimal synthesis of the minimal state-space model is developed so as to minimize the l₂-sensitivity subject to l₂-scaling constraints. Finally, a numerical example is given to demonstrate the validity and effectiveness of the proposed technique.