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Cascade-form odd-order stability-guaranteed tunable-bandwidth digital filter

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Abstract

This paper reveals a stability-constrained approach for designing an odd-order recursive digital filter whose frequency bandwidths are freely tunable. The tunable filter has a cascade structure, and it also has definitely ensured stability. The odd-order tunable-bandwidth (OO-TBW) filter consists of a single first-order (1st-order) recursive section and a few second-order (2nd-order) recursive sections. Those sections are cascaded together to form the overall OO-TBW filter. To ensure that the cascade-form OO-TBW filter is definitely stable, a strategic technique is adopted, which expresses the coefficients of both the single 1st-order and multiple 2nd-order sections as a kind of specifically-defined composite functions. With such specific parameterizations, the resulting cascade-form OO-TBW filter is able to meet the stability requirement definitely. As a result, the resulting OO-TBW filter not only has an odd-order cascade structure, but its stability issue is resolved. To demonstrate the ensured stability and also the significantly high accuracy of the resultant OO-TBW filter, a lowpass OO-TBW filter (tunable-bandwidth lowpass filter) is designed, and the simulation results are detailed and analyzed.

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References

  1. Indrakanti, R., Elias, E.: Design of low-complexity Farrow structure-based reconfigurable filters for parallel spectrum hole detection. Signal Image Video Process. 13, 787–794 (2019). https://doi.org/10.1007/s11760-019-01414-7

    Article  Google Scholar 

  2. Sutthikarn, P., Chivapreecha, S., Trirat, A., Jongsataporn, T.: A simple tunable biquadratic digital bandpass filter design for spectrum sensing in cognitive radio. Proc. IEEE ECTI-CON 2020, 71–75 (2020)

    Google Scholar 

  3. Deng, T.-B.: Design and parallel implementation of FIR digital filters with simultaneously variable magnitude and non-integer phase-delay responses. IEEE Trans. Circuits Syst. II Analog and Digital Signal Process. 50(5), 243–250 (2003)

    Article  Google Scholar 

  4. Deng, T.-B.: Closed-form design and efficient implementation of variable digital filters with simultaneously tunable magnitude and fractional-delay. IEEE Trans. Signal Process. 52(6), 1668–1681 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  5. Zarour, R., Fahmy, M.M.: A design technique for variable digital filters. IEEE Trans. Circuits Syst. 36(11), 1473–1478 (1989)

    Article  MathSciNet  Google Scholar 

  6. Zarour, R., Fahmy, M.M.: A design technique for variable two-dimensional recursive digital filters. Signal Process. 17(2), 175–182 (1989)

    Article  Google Scholar 

  7. Hussein, A.O., Fahmy, M.M.: Design of 2-D linear phase variable recursive digital filters for parallel form implementation. IEE Proc.-G 138(3), 335–340 (1991)

    Google Scholar 

  8. Deng, T.-B.: Design of recursive 1-D variable filters with guaranteed stability. IEEE Trans. Circuits Syst. II. Analog Digit. Signal Process. 44(9), 689–695 (1997)

    Article  Google Scholar 

  9. Deng, T.-B.: Design of recursive variable-digital-filters with theoretically-guaranteed stability. Int. J. Electron. 103(12), 2013–2028 (2016)

    Article  Google Scholar 

  10. Jackson, L.B.: Digital Filters and Signa Processing, 2nd edn. Kluwer Academic Publishers, Amsterdam (1992)

    Google Scholar 

  11. Deng, T.-B.: Variable-bandwidth recursive-filter design employing cascaded stability-guaranteed 2nd-order sections using coefficient transformations. J. Inf. Telecommun. (2023). https://doi.org/10.1080/24751839.2023.2267890

    Article  Google Scholar 

  12. Deng, T.-B.: Typical benchmark specifications for designing stable variable filters using novel unity-bounded functions. Vietnam J. Comput. Sci. (2023). https://doi.org/10.1142/S2196888823400018

    Article  Google Scholar 

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  1. Faculty of Science, Toho University, Miyama 2-2-1, Funabashi, 274-8510, Chiba, Japan

    Tian-Bo Deng

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  1. Tian-Bo Deng
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Deng, TB. Cascade-form odd-order stability-guaranteed tunable-bandwidth digital filter. SIViP 18, 2773–2781 (2024). https://doi.org/10.1007/s11760-023-02948-7

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  • DOI: https://doi.org/10.1007/s11760-023-02948-7

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