Omar, A.; Shpak, D.; Agathoklis, P. Nearly Linear-Phase 2-D Recursive Digital Filters Design Using Balanced Realization Model Reduction. Signals2023, 4, 800-815.
Omar, A.; Shpak, D.; Agathoklis, P. Nearly Linear-Phase 2-D Recursive Digital Filters Design Using Balanced Realization Model Reduction. Signals 2023, 4, 800-815.
Omar, A.; Shpak, D.; Agathoklis, P. Nearly Linear-Phase 2-D Recursive Digital Filters Design Using Balanced Realization Model Reduction. Signals2023, 4, 800-815.
Omar, A.; Shpak, D.; Agathoklis, P. Nearly Linear-Phase 2-D Recursive Digital Filters Design Using Balanced Realization Model Reduction. Signals 2023, 4, 800-815.
Abstract
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.
Keywords
2-D IIR digital filters; Structured Gramians; Lyapunov inequalities; Linear matrix inequalities(LMI); Balanced truncation
Subject
Engineering, Electrical and Electronic Engineering
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
