Roundoff Noise Analysis for Generalized Direct-Form II Structure of 2-D Separable-Denominator Digital Filters

Based on the concept of polynomial operators, generalized direct-form II structure of two-dimensional (2-D) separable-denominator (SD) digital filters is explored. It is shown that 2-D SD digital filters can be modeled by a generalized SIMO direct- form II and a generalized MISO transposed direct-form II that are connected in cascade. Then an expression for the roundoff noise gain in the resulting structure is derived and investigated. Moreover, the roundoff noise gain is compared with that deduced in a recent study of generalized direct-form II realization of 2-D SD digital filters.