A Nonlinear Optimization Design Algorithm for Nearly Linear-Phase 2D IIR Digital Filters
In this paper, a new optimization method for the design of nearly linear-phase two-dimensional infinite impulse (2D IIR) digital filters with a separable denominator is proposed. A design framework for 2D IIR digital filters is formulated as a nonlinear constrained optimization problem where the gro...
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MDPI AG
2023-08-01
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| Online Access: | https://www.mdpi.com/2624-6120/4/3/30 |
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| author | Abdussalam Omar Dale Shpak Panajotis Agathoklis Belaid Moa |
| author_facet | Abdussalam Omar Dale Shpak Panajotis Agathoklis Belaid Moa |
| author_sort | Abdussalam Omar |
| collection | DOAJ |
| description | In this paper, a new optimization method for the design of nearly linear-phase two-dimensional infinite impulse (2D IIR) digital filters with a separable denominator is proposed. A design framework for 2D IIR digital filters is formulated as a nonlinear constrained optimization problem where the group delay deviation in the passband is minimized under prescribed soft magnitude constraints and hard stability requirements. To achieve this goal, sub-level sets of the group delay deviations are utilized to generate a sequence of filters, from which the one with the best performance is selected. The quality of the obtained filter is evaluated using three quality factors, namely, the passband magnitude quality factor <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>Q</mi><mi>h</mi></msub></semantics></math></inline-formula> and the group delay deviation quality factor <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>Q</mi><mi>τ</mi></msub></semantics></math></inline-formula>, while the third one is a new quality factor <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>Q</mi><mi>s</mi></msub></semantics></math></inline-formula> that assesses the performance in the stopband relative to the minimum filter gain in the passband. The proposed framework is implemented using the interior-point (IP) method in a MATLAB environment, and the experimental results show that filters designed using the proposed method have good magnitude response and low group delay deviation. The performance of the resulting filters is compared with the results of other methods. |
| first_indexed | 2024-03-10T22:00:12Z |
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| institution | Directory Open Access Journal |
| issn | 2624-6120 |
| language | English |
| last_indexed | 2024-03-10T22:00:12Z |
| publishDate | 2023-08-01 |
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| spelling | doaj.art-2f8a17bcc9244a008b21beade7dfd8b72023-11-19T12:58:26ZengMDPI AGSignals2624-61202023-08-014357559010.3390/signals4030030A Nonlinear Optimization Design Algorithm for Nearly Linear-Phase 2D IIR Digital FiltersAbdussalam Omar0Dale Shpak1Panajotis Agathoklis2Belaid Moa3Department of Electrical and Computer Engineering, University of Victoria, Victoria, BC V8W 3P6, CanadaDepartment of Electrical and Computer Engineering, University of Victoria, Victoria, BC V8W 3P6, CanadaDepartment of Electrical and Computer Engineering, University of Victoria, Victoria, BC V8W 3P6, CanadaDepartment of Electrical and Computer Engineering, University of Victoria, Victoria, BC V8W 3P6, CanadaIn this paper, a new optimization method for the design of nearly linear-phase two-dimensional infinite impulse (2D IIR) digital filters with a separable denominator is proposed. A design framework for 2D IIR digital filters is formulated as a nonlinear constrained optimization problem where the group delay deviation in the passband is minimized under prescribed soft magnitude constraints and hard stability requirements. To achieve this goal, sub-level sets of the group delay deviations are utilized to generate a sequence of filters, from which the one with the best performance is selected. The quality of the obtained filter is evaluated using three quality factors, namely, the passband magnitude quality factor <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>Q</mi><mi>h</mi></msub></semantics></math></inline-formula> and the group delay deviation quality factor <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>Q</mi><mi>τ</mi></msub></semantics></math></inline-formula>, while the third one is a new quality factor <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>Q</mi><mi>s</mi></msub></semantics></math></inline-formula> that assesses the performance in the stopband relative to the minimum filter gain in the passband. The proposed framework is implemented using the interior-point (IP) method in a MATLAB environment, and the experimental results show that filters designed using the proposed method have good magnitude response and low group delay deviation. The performance of the resulting filters is compared with the results of other methods.https://www.mdpi.com/2624-6120/4/3/30nearly linear-phase filtersgroup delay2D IIR filter design by optimization2D filter stabilityfilter design |
| spellingShingle | Abdussalam Omar Dale Shpak Panajotis Agathoklis Belaid Moa A Nonlinear Optimization Design Algorithm for Nearly Linear-Phase 2D IIR Digital Filters Signals nearly linear-phase filters group delay 2D IIR filter design by optimization 2D filter stability filter design |
| title | A Nonlinear Optimization Design Algorithm for Nearly Linear-Phase 2D IIR Digital Filters |
| title_full | A Nonlinear Optimization Design Algorithm for Nearly Linear-Phase 2D IIR Digital Filters |
| title_fullStr | A Nonlinear Optimization Design Algorithm for Nearly Linear-Phase 2D IIR Digital Filters |
| title_full_unstemmed | A Nonlinear Optimization Design Algorithm for Nearly Linear-Phase 2D IIR Digital Filters |
| title_short | A Nonlinear Optimization Design Algorithm for Nearly Linear-Phase 2D IIR Digital Filters |
| title_sort | nonlinear optimization design algorithm for nearly linear phase 2d iir digital filters |
| topic | nearly linear-phase filters group delay 2D IIR filter design by optimization 2D filter stability filter design |
| url | https://www.mdpi.com/2624-6120/4/3/30 |
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