Skip to main content

Digital Filters Optimization Modelling with Non-canonical Hypercomplex Number Systems

Part of the Advances in Intelligent Systems and Computing book series (AISC,volume 938)

Abstract

Recursive digital filter modelling is one of the tasks, which modelling can be improved by using hypercomplex numbers. Existing models are about data representation in canonical hypercomplex number system only. However, canonical number systems have some restrictions. Applying the non-canonical number systems gives more possibilities for filter simulation and its further optimization by its parametric sensitivity since they have more structure constants in Keli table.

The paper proposes a digital filter synthesis method, which is using non-canonical hypercomplex number systems. Use of non-canonical hypercomplex number system with greater number of non-zero structure constants in Keli table can significantly improve the sensitivity of the digital filter.

Keywords

  • Hypercomplex numbers
  • Non-canonical number system
  • Digital filter sensitivity
  • Filter sensitivity

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-3-030-16621-2_42
  • Chapter length: 11 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   219.00
Price excludes VAT (USA)
  • ISBN: 978-3-030-16621-2
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   279.99
Price excludes VAT (USA)
Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.

References

  1. Rajankar, O.S., Kolekar, U.D.: Scale space reduction with interpolation to speed up visual saliency detection. Int. J. Image Graph. Signal Process. (IJIGSP) 7(8), 58–65 (2015). https://doi.org/10.5815/ijigsp.2015.08.07

    CrossRef  Google Scholar 

  2. Khalil, M.I.: Applying quaternion Fourier transforms for enhancing color images. Int. J. Image Graph. Signal Process. (IJIGSP) 4(2), 9–15 (2012). https://doi.org/10.5815/ijigsp.2012.02.02

  3. Hata, R., Akhand, M.A.H., Islam, M.M., Murase, K.: Simplified real-, complex-, and quaternion-valued neuro-fuzzy learning algorithms. Int. J. Intell. Syst. Appl. (IJISA) 10(5), 1–13 (2018). https://doi.org/10.5815/ijisa.2018.05.01

    CrossRef  Google Scholar 

  4. Kumar, S., Tripathi, B.K.: On the root-power mean aggregation based neuron in quaternionic domain. Int. J. Intell. Syst. Appl. (IJISA) 10(7), 11–26 (2018). https://doi.org/10.5815/ijisa.2018.07.02

    CrossRef  Google Scholar 

  5. Kalinovsky, Y.A., Boyarinova, Y.E.: High dimensional isomorphic hypercomplex number systems and their using for calculation efficiency. Infodruk, Kyiv (2012)

    Google Scholar 

  6. Kalinovsky, J., Sinkov, M., Boyarinova, Y., Fedorenko, O., Sinkova, T.: Development of theoretical bases and toolkit for information processing in hypercomplex numerical systems. Pomiary. Automatyka. Komputery w gospodarce i ochronie srodowiska 1, 18–21 (2009)

    Google Scholar 

  7. Toyoshima, H.: Computationally efficient implementation of hypercomplex digital filters. IEICE Trans. Fundam. E85-A(8), 1870–1876 (2002)

    Google Scholar 

  8. Took, C.C., Mandic, D.P.: The quaternion LMS algorithm for adaptive filtering of hypercomplex processes. IEEE Trans. Signal Process. 57(4), 1316–1327 (2009)

    MathSciNet  CrossRef  Google Scholar 

  9. Kalinovsky, Y.O., Lande, D.V., Boyarinova, Y.E., Khitsko, I.V.: Infinite hypercomplex number system factorization methods. http://arxiv.org/abs/1401.2844 (2014)

  10. Sinkov, M.V., Kalinovsky, Y.A., Boyarinova, Y.E.: Finite-Dimensional Hypercomplex Numerical Systems. Theory Basis. Supplement, Infodruk, Кyiv (2010)

    Google Scholar 

  11. Sinkov, M.V., Kalinovskiy, J.A., Boyarinova, Y.E., Sinkova, T.V., Fedorenko, O.V., Gorodko, N.O.: Fundamental principles of effective data presentation and processing on the basis of hypercomplex numerical systems. Data Rec. Storage Process. 12(2), 62–68 (2010)

    Google Scholar 

  12. Kalinosky, Y.A., Fedorenko, O.V.: Principles of constructing digital filters with hypercomplex coefficients. Data Rec. Storage Process. 11(1), 52–59 (2009)

    Google Scholar 

  13. Fedorenko, O.V.: Digital filters with low parametric sensitivity. Data Rec. Storage Process. 10(2), 87–94 (2008)

    Google Scholar 

  14. Kalinovsky, Y.O., Boyarinova, Y.E., Khitsko, I.V.: Reversible digital filters total parametric sensitivity optimization using non-canonical hypercomplex number systems (2015). http://arxiv.org/abs/1506.01701

  15. Kalinovsky, Y.O., Boyarinova, Y.E., Khitsko, I.V.: Hypercomplex operations system in Maple. Data Rec. Storage Process. 19(2), 11–23 (2017)

    Google Scholar 

  16. Kalinovsky, Y.O., Boyarinova, Y.E., Khitsko, I.V.: Software complex for hypercomplex computing. Electron. Model. 39(5), 81–95 (2017)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Iana Khitsko .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this paper

Verify currency and authenticity via CrossMark

Cite this paper

Kalinovsky, Y., Boyarinova, Y., Khitsko, I., Oleshchenko, L. (2020). Digital Filters Optimization Modelling with Non-canonical Hypercomplex Number Systems. In: Hu, Z., Petoukhov, S., Dychka, I., He, M. (eds) Advances in Computer Science for Engineering and Education II. ICCSEEA 2019. Advances in Intelligent Systems and Computing, vol 938. Springer, Cham. https://doi.org/10.1007/978-3-030-16621-2_42

Download citation