Quantization error calculation of various realizations of 2-D separable-in-denominator recursive filters

This paper provides an effective method to evaluate the input quantization and multiplication roundoff errors for two-dimensional (2-D) separable-in-denominator recursive digital (SDRD) filters. This work is based on the partial fraction expansion of 2-D SDRD filters [1] and their modular implementation structures [2] proposed by the authors. Equations are derived for the calculation of roundoff errors for various implementations of 2-D SDRD filters. An example is given to demonstrate the application of the proposed method.