Nearly Linear-Phase 2-D Recursive Digital Filters Design using Balanced Realization Model Reduction

This paper presents a new method for the design of separable denominators 2-D IIR filters with nearly linear phase in the passband. The design method is based on a balanced-realization model reduction technique. The nearly linear-phase 2-D IIR filter is designed using 2-D model reduction from a linear-phase 2-D FIR filter, which serves as the initial filter. The structured controllability and observability Gramians $P^s$ and $Q^s$ serve as the foundation for this technique. These Gramians are block diagonal positive-definite matrices that satisfy 2-D Lyapunov equations. An efficient method is used to compute these Gramians by minimizing the traces of $P^s$ and $Q^s$ under linear matrix inequalities (LMI) constraints. The use of these Gramians ensures that the resulting 2-D IIR filter preserves stability and can be implemented using a separable denominator 2-D filter with fewer coefficients than the original 2-D FIR filter. Numerical examples show that the proposed method compares favorably with existing techniques.