Advertisement

Digital Filters Optimization Modelling with Non-canonical Hypercomplex Number Systems

  • Yakiv Kalinovsky
  • Yuliya Boyarinova
  • Iana KhitskoEmail author
  • Liubov Oleshchenko
Conference paper
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 

References

  1. 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.2015.08.07CrossRefGoogle Scholar
  2. 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. 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.2018.05.01CrossRefGoogle Scholar
  4. 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.2018.07.02CrossRefGoogle Scholar
  5. 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. 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. 7.
    Toyoshima, H.: Computationally efficient implementation of hypercomplex digital filters. IEICE Trans. Fundam. E85-A(8), 1870–1876 (2002)Google Scholar
  8. 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)MathSciNetCrossRefGoogle Scholar
  9. 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. 10.
    Sinkov, M.V., Kalinovsky, Y.A., Boyarinova, Y.E.: Finite-Dimensional Hypercomplex Numerical Systems. Theory Basis. Supplement, Infodruk, Кyiv (2010)Google Scholar
  11. 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. 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. 13.
    Fedorenko, O.V.: Digital filters with low parametric sensitivity. Data Rec. Storage Process. 10(2), 87–94 (2008)Google Scholar
  14. 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. 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. 16.
    Kalinovsky, Y.O., Boyarinova, Y.E., Khitsko, I.V.: Software complex for hypercomplex computing. Electron. Model. 39(5), 81–95 (2017)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Yakiv Kalinovsky
    • 1
  • Yuliya Boyarinova
    • 2
  • Iana Khitsko
    • 2
    Email author
  • Liubov Oleshchenko
    • 2
  1. 1.Institute for Information RecordingNational Academy of Science of UkraineKyivUkraine
  2. 2.National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”KyivUkraine

Personalised recommendations