Omar, AbdussalamShpak, DaleAgathoklis, Panajotis2023-12-082023-12-0820232023Omar, A., Shpak, D., & Agathoklis, P. (2023). Nearly Linear-Phase 2-D Recursive Digital Filters Design Using Balanced Realization Model Reduction. Signals, 4(4), 800–815. https://doi.org/10.3390/signals4040044https://doi.org/10.3390/signals4040044http://hdl.handle.net/1828/15692This paper presents a new method for the design of separable-denominator 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. onal 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 inequality (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.enAttribution 2.5 Canada2-D IIR digital filtersstructured GramiansLyapunov inequalitieslinear matrix inequalities (LMI)balanced truncationArticleDepartment of Electrical and Computer Engineering