Analysis of roundoff noise in separable‐denominator two‐dimensional digital filters

A tradeoff among filter wordlength, processing precision, and processing speed, is an important subject in realtime twodimensional (2‐D) digital filtering. This paper analyzes the roundoff noise in implementing separable‐denominator 2‐D digital filters with finite wordlength. Separable‐denominator 2‐D digital filters with infinite and finite wordlength are described by Roesser's state space model. The output error variance due to roundoff noise in 2‐D digital filters with finite wordlength is obtained in the state‐space formulation. It is shown via equivalent transformations that the output error variance due to roundoff noise in 2‐D digital filters depends slightly on filter structures. The l₂‐norm of 2‐D digital filters is defined, and the l₂‐norm scaling is introduced to fully utilize the dynamic range without causing excessive overflows. Finally, the validity of the proposed analysis method of the roundoff noise in separable‐denominator 2‐D digital filters and the structural dependency of the roundoff noise are clarified through numerical examples.