The analysis of conditions for preservation of gain-frequency and phase-frequency characteristics optimality under analog and digital filters transformation
Prototype filters have wide usage for the design of filters with required quality indexes (QI) of gain-frequency response (GFR). The designed filter is obtained from a prototype filter b means of frequency transformation, which preserves these QI. But most of employed frequency transformations resul...
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MIREA - Russian Technological University
2020-04-01
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| Series: | Российский технологический журнал |
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| Online Access: | https://www.rtj-mirea.ru/jour/article/view/210 |
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| author | A. V. Smirnov |
| author_facet | A. V. Smirnov |
| author_sort | A. V. Smirnov |
| collection | DOAJ |
| description | Prototype filters have wide usage for the design of filters with required quality indexes (QI) of gain-frequency response (GFR). The designed filter is obtained from a prototype filter b means of frequency transformation, which preserves these QI. But most of employed frequency transformations result in variations of QI of phase-frequency response (PFR). In this paper we proposed to use prototype filters that are Pareto-optimal for QI of GFR and PFR. Transfer functions of these filters may be found by means of heuristic optimization algorithms. This method will be efficient if the frequency transformation preserves the optimality of filters. It was shown that frequency transformation has this feature if it preserves the result of QI comparison (more or less) for filters with equal orders. Compliance of this criterion was checked for bilinear transformation of analog low pass filters (LPF) into digital LPF and for Konstantinidis transformation of digital LPF into other digital LPF. The analysis showed that Pareto-optimality for QI of GFR and PFR is preserved if the delay-frequency characteristic of the filter has a minimum at zero frequency and has a maximum at the upper boundary of the pass band. These conditions are complied for LPF with sufficiently small unevenness of GFR in the pass band and sufficiently fast decline of GFR at higher frequencies. Examples confirming these conclusions are given. |
| format | Article |
| id | doaj-art-d3966c7d9d70434abbff327b99c31f8e |
| institution | Kabale University |
| issn | 2500-316X |
| language | Russian |
| publishDate | 2020-04-01 |
| publisher | MIREA - Russian Technological University |
| record_format | Article |
| series | Российский технологический журнал |
| spelling | doaj-art-d3966c7d9d70434abbff327b99c31f8e2025-02-03T11:45:49ZrusMIREA - Russian Technological UniversityРоссийский технологический журнал2500-316X2020-04-0182435810.32362/2500-316X-2020-8-2-43-58197The analysis of conditions for preservation of gain-frequency and phase-frequency characteristics optimality under analog and digital filters transformationA. V. Smirnov0MIREA – Russia Technological UniversityPrototype filters have wide usage for the design of filters with required quality indexes (QI) of gain-frequency response (GFR). The designed filter is obtained from a prototype filter b means of frequency transformation, which preserves these QI. But most of employed frequency transformations result in variations of QI of phase-frequency response (PFR). In this paper we proposed to use prototype filters that are Pareto-optimal for QI of GFR and PFR. Transfer functions of these filters may be found by means of heuristic optimization algorithms. This method will be efficient if the frequency transformation preserves the optimality of filters. It was shown that frequency transformation has this feature if it preserves the result of QI comparison (more or less) for filters with equal orders. Compliance of this criterion was checked for bilinear transformation of analog low pass filters (LPF) into digital LPF and for Konstantinidis transformation of digital LPF into other digital LPF. The analysis showed that Pareto-optimality for QI of GFR and PFR is preserved if the delay-frequency characteristic of the filter has a minimum at zero frequency and has a maximum at the upper boundary of the pass band. These conditions are complied for LPF with sufficiently small unevenness of GFR in the pass band and sufficiently fast decline of GFR at higher frequencies. Examples confirming these conclusions are given.https://www.rtj-mirea.ru/jour/article/view/210analog filterdigital filterquality indexfrequency transformationgain-frequency responsephase-frequency responsepareto-optimality |
| spellingShingle | A. V. Smirnov The analysis of conditions for preservation of gain-frequency and phase-frequency characteristics optimality under analog and digital filters transformation Российский технологический журнал analog filter digital filter quality index frequency transformation gain-frequency response phase-frequency response pareto-optimality |
| title | The analysis of conditions for preservation of gain-frequency and phase-frequency characteristics optimality under analog and digital filters transformation |
| title_full | The analysis of conditions for preservation of gain-frequency and phase-frequency characteristics optimality under analog and digital filters transformation |
| title_fullStr | The analysis of conditions for preservation of gain-frequency and phase-frequency characteristics optimality under analog and digital filters transformation |
| title_full_unstemmed | The analysis of conditions for preservation of gain-frequency and phase-frequency characteristics optimality under analog and digital filters transformation |
| title_short | The analysis of conditions for preservation of gain-frequency and phase-frequency characteristics optimality under analog and digital filters transformation |
| title_sort | analysis of conditions for preservation of gain frequency and phase frequency characteristics optimality under analog and digital filters transformation |
| topic | analog filter digital filter quality index frequency transformation gain-frequency response phase-frequency response pareto-optimality |
| url | https://www.rtj-mirea.ru/jour/article/view/210 |
| work_keys_str_mv | AT avsmirnov theanalysisofconditionsforpreservationofgainfrequencyandphasefrequencycharacteristicsoptimalityunderanaloganddigitalfilterstransformation AT avsmirnov analysisofconditionsforpreservationofgainfrequencyandphasefrequencycharacteristicsoptimalityunderanaloganddigitalfilterstransformation |