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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
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
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
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
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
Kalinovsky, Y.A., Boyarinova, Y.E.: High dimensional isomorphic hypercomplex number systems and their using for calculation efficiency. Infodruk, Kyiv (2012)
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)
Toyoshima, H.: Computationally efficient implementation of hypercomplex digital filters. IEICE Trans. Fundam. E85-A(8), 1870–1876 (2002)
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)
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)
Sinkov, M.V., Kalinovsky, Y.A., Boyarinova, Y.E.: Finite-Dimensional Hypercomplex Numerical Systems. Theory Basis. Supplement, Infodruk, Кyiv (2010)
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)
Kalinosky, Y.A., Fedorenko, O.V.: Principles of constructing digital filters with hypercomplex coefficients. Data Rec. Storage Process. 11(1), 52–59 (2009)
Fedorenko, O.V.: Digital filters with low parametric sensitivity. Data Rec. Storage Process. 10(2), 87–94 (2008)
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
Kalinovsky, Y.O., Boyarinova, Y.E., Khitsko, I.V.: Hypercomplex operations system in Maple. Data Rec. Storage Process. 19(2), 11–23 (2017)
Kalinovsky, Y.O., Boyarinova, Y.E., Khitsko, I.V.: Software complex for hypercomplex computing. Electron. Model. 39(5), 81–95 (2017)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
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
DOI: https://doi.org/10.1007/978-3-030-16621-2_42
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-16620-5
Online ISBN: 978-3-030-16621-2
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)