Design of low‐pass and band‐pass infinite impulse response maximally flat stable digital differentiators
Abstract Maximally flat digital differentiators (MFDDs) are very attractive for differentiation of narrowband signals. The design of infinite impulse response (IIR) MFDDs, however, is very challenging due to the non‐convexity of the flatness constraints of the IIR digital differentiator (DD). This s...
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| Format: | Article |
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Wiley
2022-04-01
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| Series: | IET Signal Processing |
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| Online Access: | https://doi.org/10.1049/sil2.12084 |
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| author | Huoping Yi Xiaoping Lai |
| author_facet | Huoping Yi Xiaoping Lai |
| author_sort | Huoping Yi |
| collection | DOAJ |
| description | Abstract Maximally flat digital differentiators (MFDDs) are very attractive for differentiation of narrowband signals. The design of infinite impulse response (IIR) MFDDs, however, is very challenging due to the non‐convexity of the flatness constraints of the IIR digital differentiator (DD). This study derives a set of linear conditions that are equivalent to the non‐convex flatness constraints and then utilises these conditions to design low‐pass and band‐pass IIR MFDDs with low and nearly constant group delay. In addition, a generalized‐positive‐realness‐based stability constraint is incorporated in the design to ensure the robust stability of the DD. A design algorithm is presented to maximise the total flatness degree subject to the flatness conditions and the stability constraint, resulting in maximally flat stable DDs (MFSDDs). Design examples and comparisons with existing DDs demonstrate that the designed IIR MFSDDs have better magnitude and group‐delay responses and lower implementation complexity. |
| format | Article |
| id | doaj-art-e6584f80b4864616a5c47d1c2cf97b0e |
| institution | Kabale University |
| issn | 1751-9675 1751-9683 |
| language | English |
| publishDate | 2022-04-01 |
| publisher | Wiley |
| record_format | Article |
| series | IET Signal Processing |
| spelling | doaj-art-e6584f80b4864616a5c47d1c2cf97b0e2025-02-03T01:29:36ZengWileyIET Signal Processing1751-96751751-96832022-04-0116220121910.1049/sil2.12084Design of low‐pass and band‐pass infinite impulse response maximally flat stable digital differentiatorsHuoping Yi0Xiaoping Lai1Institute of Information and Control Hangzhou Dianzi University Hangzhou ChinaInstitute of Information and Control Hangzhou Dianzi University Hangzhou ChinaAbstract Maximally flat digital differentiators (MFDDs) are very attractive for differentiation of narrowband signals. The design of infinite impulse response (IIR) MFDDs, however, is very challenging due to the non‐convexity of the flatness constraints of the IIR digital differentiator (DD). This study derives a set of linear conditions that are equivalent to the non‐convex flatness constraints and then utilises these conditions to design low‐pass and band‐pass IIR MFDDs with low and nearly constant group delay. In addition, a generalized‐positive‐realness‐based stability constraint is incorporated in the design to ensure the robust stability of the DD. A design algorithm is presented to maximise the total flatness degree subject to the flatness conditions and the stability constraint, resulting in maximally flat stable DDs (MFSDDs). Design examples and comparisons with existing DDs demonstrate that the designed IIR MFSDDs have better magnitude and group‐delay responses and lower implementation complexity.https://doi.org/10.1049/sil2.12084Digital filtersIIR filtersLow‐pass filtersBand‐pass filtersFIR filters |
| spellingShingle | Huoping Yi Xiaoping Lai Design of low‐pass and band‐pass infinite impulse response maximally flat stable digital differentiators IET Signal Processing Digital filters IIR filters Low‐pass filters Band‐pass filters FIR filters |
| title | Design of low‐pass and band‐pass infinite impulse response maximally flat stable digital differentiators |
| title_full | Design of low‐pass and band‐pass infinite impulse response maximally flat stable digital differentiators |
| title_fullStr | Design of low‐pass and band‐pass infinite impulse response maximally flat stable digital differentiators |
| title_full_unstemmed | Design of low‐pass and band‐pass infinite impulse response maximally flat stable digital differentiators |
| title_short | Design of low‐pass and band‐pass infinite impulse response maximally flat stable digital differentiators |
| title_sort | design of low pass and band pass infinite impulse response maximally flat stable digital differentiators |
| topic | Digital filters IIR filters Low‐pass filters Band‐pass filters FIR filters |
| url | https://doi.org/10.1049/sil2.12084 |
| work_keys_str_mv | AT huopingyi designoflowpassandbandpassinfiniteimpulseresponsemaximallyflatstabledigitaldifferentiators AT xiaopinglai designoflowpassandbandpassinfiniteimpulseresponsemaximallyflatstabledigitaldifferentiators |