On the Design of Power Law Filters and Their Inverse Counterparts
This paper presents the optimal modeling of Power Law Filters (PLFs) with the low-pass (LP), high-pass (HP), band-pass (BP), and band-stop (BS) responses by means of rational approximants. The optimization is performed for three different objective functions and second-order filter mother functions....
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-11-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/5/4/197 |
| _version_ | 1827672395563925504 |
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| author | Shibendu Mahata Norbert Herencsar David Kubanek |
| author_facet | Shibendu Mahata Norbert Herencsar David Kubanek |
| author_sort | Shibendu Mahata |
| collection | DOAJ |
| description | This paper presents the optimal modeling of Power Law Filters (PLFs) with the low-pass (LP), high-pass (HP), band-pass (BP), and band-stop (BS) responses by means of rational approximants. The optimization is performed for three different objective functions and second-order filter mother functions. The formulated design constraints help avoid placement of the zeros and poles on the right-half <i>s</i>-plane, thus, yielding stable PLF and inverse PLF (IPLF) models. The performances of the approximants exhibiting the fractional-step magnitude and phase responses are evaluated using various statistical indices. At the cost of higher computational complexity, the proposed approach achieved improved accuracy with guaranteed stability when compared to the published literature. The four types of optimal PLFs and IPLFs with an exponent <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> of 0.5 are implemented using the follow-the-leader feedback topology employing AD844AN current feedback operational amplifiers. The experimental results demonstrate that the Total Harmonic Distortion achieved for all the practical PLF and IPLF circuits was equal or lower than 0.21%, whereas the Spurious-Free Dynamic Range also exceeded 57.23 and 54.72 dBc, respectively. |
| first_indexed | 2024-03-10T04:05:49Z |
| format | Article |
| id | doaj.art-f241fbec6a7a4c969e4196667441261b |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-10T04:05:49Z |
| publishDate | 2021-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-f241fbec6a7a4c969e4196667441261b2023-11-23T08:23:37ZengMDPI AGFractal and Fractional2504-31102021-11-015419710.3390/fractalfract5040197On the Design of Power Law Filters and Their Inverse CounterpartsShibendu Mahata0Norbert Herencsar1David Kubanek2Department of Electrical Engineering, Dr. B. C. Roy Engineering College, Durgapur 713206, PO, IndiaDepartment of Telecommunications, Faculty of Electrical Engineering and Communication, Brno University of Technology, Technicka 12, 61600 Brno, Czech RepublicDepartment of Telecommunications, Faculty of Electrical Engineering and Communication, Brno University of Technology, Technicka 12, 61600 Brno, Czech RepublicThis paper presents the optimal modeling of Power Law Filters (PLFs) with the low-pass (LP), high-pass (HP), band-pass (BP), and band-stop (BS) responses by means of rational approximants. The optimization is performed for three different objective functions and second-order filter mother functions. The formulated design constraints help avoid placement of the zeros and poles on the right-half <i>s</i>-plane, thus, yielding stable PLF and inverse PLF (IPLF) models. The performances of the approximants exhibiting the fractional-step magnitude and phase responses are evaluated using various statistical indices. At the cost of higher computational complexity, the proposed approach achieved improved accuracy with guaranteed stability when compared to the published literature. The four types of optimal PLFs and IPLFs with an exponent <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> of 0.5 are implemented using the follow-the-leader feedback topology employing AD844AN current feedback operational amplifiers. The experimental results demonstrate that the Total Harmonic Distortion achieved for all the practical PLF and IPLF circuits was equal or lower than 0.21%, whereas the Spurious-Free Dynamic Range also exceeded 57.23 and 54.72 dBc, respectively.https://www.mdpi.com/2504-3110/5/4/197analog filter approximationanalog signal processingfractional-order filterinverse filter |
| spellingShingle | Shibendu Mahata Norbert Herencsar David Kubanek On the Design of Power Law Filters and Their Inverse Counterparts Fractal and Fractional analog filter approximation analog signal processing fractional-order filter inverse filter |
| title | On the Design of Power Law Filters and Their Inverse Counterparts |
| title_full | On the Design of Power Law Filters and Their Inverse Counterparts |
| title_fullStr | On the Design of Power Law Filters and Their Inverse Counterparts |
| title_full_unstemmed | On the Design of Power Law Filters and Their Inverse Counterparts |
| title_short | On the Design of Power Law Filters and Their Inverse Counterparts |
| title_sort | on the design of power law filters and their inverse counterparts |
| topic | analog filter approximation analog signal processing fractional-order filter inverse filter |
| url | https://www.mdpi.com/2504-3110/5/4/197 |
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