Efficient Orthogonal Bicomplex Bilinear DSP Algorithm Design
DOI:
https://doi.org/10.2478/ecce-2020-0005Keywords:
Bicomplex digital filters, Orthogonal complex digital filter, Sensitivity, Word-lengthAbstract
The present paper describes the development of a new technique for designing orthogonal bicomplex Digital Signal Processing (DSP) algorithms. In contrast to those previously reported on, this novel method is of universal application while being unaffected by either the type or the order of the real digital processing algorithm employed as a prototype. The proposed technique builds on Watanabe and Nishihara’s complex orthogonal transformation, and converts real or complex orthogonal transfer functions into bicomplex orthogonal ones. In this study, the new technique is applied to the design and testing of orthogonal bilinear bicomplex filters with a canonical number of elements, the main advantage of which is that they are several times lower in order. In this way, bilinear bicomplex orthogonal transfer functions are made up of real coefficient ones of the fourth-order, thereby reducing the order of the filter by a factor of four. The experiments demonstrate that the properties of the prototype filter are acquired by the bicomplex orthogonal filters, irrespective of the prototype being complex or real in nature.References
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H. D. Schutte and J. Wenzel, “Hypercomplex numbers in digital signal processing”, Proc. IEEE Singapore International Symposium on Circuits and Systems, pp. 1557–1560, 1990.
Z. Nikolova, G. Stoyanov, G. Iliev, and V. Poulkov, “Complex coefficient IIR digital filters,” Chapter 9 in Digital Filters, F. P. G. Márquez, Ed., InTechOpen, 2011, pp. 209–239. https://doi.org/10.5772/648
T. Bulow and G. Sommer, “Hypercomplex signals – a novel extension of the analytic signals to the multidimensional case”, IEEE Transaction on Signal Processing, vol. 49, no. 11, Nov. 2001, pp. 2844–2852. https://doi.org/10.1109/78.960432
A. Khatabi, A. Tmiri, and A. Serhir, “Quaternion angular radial transform and properties transformation for color-based object recognition”, Pattern Recognition and Image Analysis, vol. 26, no. 4, 1 Oct. 2016, pp. 705–713. https://doi.org/10.1134/S1054661816040064
V. G. Labunets, E. V. Labunets, K. Egazarian and J. Astola, “Hypercomplex moments application in invariant image recognition”, Proc. of International Conference on Image Processing (ICIP98), Chicago, USA, 1998, vol. 2, pp. 257–261.
W. K. Wong, G. C. Lee, C. K. Loo and R. Lock, “Quaternion based fuzzy neural network classifier for MPIK dataset’s view-invariant color face image recognition”, Informatica (Slovenia), vol. 37, no. 2, 2013, pp. 181–192.
C. Evans, S. J. Sangwine, and T. A. Ell, “Hypercomplex color-sensitive smoothing filters”, Proc. of International Conference of Image Processing, vol. 1, pp. 541–544, 2000.
F. Tao, and W. Qian, “Image hash authentication algorithm for orthogonal moments of fractional order chaotic scrambling coupling hyper-complex number”, Measurement, vol. 134, Feb. 2019, pp. 866–873.https://doi.org/10.1016/j.measurement.2018.11.079
C. E. Moxey, S. J. Sangwine, and T. A. Ell, “Color-grayscale image registration using hypercomplex phase correlation”, Proc. of International Conference on Image Processing, vol. 2, pp. II-385–II-388, 22–25 Sept. 2002.
S. J. Sangwine and T. A. Ell, “Hypercomplex auto- and cross-correlation of color images”, Proceedings of IEEE International Conference on Image Processing (ICIP99), 24–28 Oct. 1999, Kobe, Japan, pp. 319–322.
S. J. Sangwine et al., “Color image filters based on hypercomplex convolution”, IEEE Proc. Vis. Image Signal Processing, vol. 147, no. 2, pp. 89–93, April 2000. https://doi.org/10.1049/ip-vis:20000211
L. Lu, X. Zhang, and X. Xu, “Hypercomplex extreme learning machine with its application in multispectral palmprint recognition”, PLoS ONE, vol. 14, no. 4, April 2019. https://doi.org/10.1371/journal.pone.0209083
V. Dimitrov, T. Cooklev and B. Donevsky, “On the multiplication of reduced biquaternion and applications”. Information Processing Letters, vol. 43, no. 3, pp. 161–164, 1992. https://doi.org/10.1016/0020-0190(92)90009-K
H. Toyoshima, “Computationally Efficient implementation of hypercomplex digital filters”, IEICE Trans. Fundamentals, vol. E85-A, no. 8, pp. 1870–1876, August 2002.
K. Ueda and S.-I. Takahashi, “Strictly proper digital filters with hypercomplex coefficients”, Proc. ECCTD’93 European Conference on Circuit Theory & Design, pp. 739–744, Sept. 1993.
K. Ueda, K. Mazukami, and S.-I. Takahashi, “Realization of complex coefficient digital filters based on hypercomplex arithmetic”, Proc. European Signal Processing Conference (EUROSIPCO’94), pp. 363–366, Sept. 1994.
H. Osaco, K. Ueda, and S.-I. Takahashi, “Digital filter with eight elements hypercomplex coefficient”, Proc. of 12th European Conference on Circuit Theory & Design (ECCTD’95), ITU, Istanbul Technical University, Istanbul, Turkey, August 1995, pp. 659–662.
D. Alfsmann, and H. G. Göckler, “Hypercomplex Bark-scale filter bank design based on allpass-phase specifications”, European Signal Processing Conference, EUSIPCO 2012, Bucharest, Romania, 27–31 August 2012, pp. 519–523.
Y. N. Li, “Quaternion polar harmonic transforms for color images”, IEEE Signal Processing Letters, vol. 20, no. 8, 2013, 6530686, pp. 803–806. https://doi.org/10.1109/LSP.2013.2267775
B. Hu, Y. Zhou, L.-D. Li, J.-Y. Zhang and J.-S. Pan, “Polar linear canonical transform in quaternion domain”, Journal of Information Hiding and Multimedia Signal Processing, vol. 6, no. 6, 2015, pp. 1185–1193.
M. Kamata, and S.-I. Takahashi, “Orthogonal filter with hypercomplex coefficients, including cases of complex and real ones”, Proc. of ECCTD’97, Budapest, Hungary, Sept. 1997, pp. 594–598.
M. Okuda, M. Kamata, and S.-I. Takahashi, “Realization of an orthogonal filter with hypercomplex coefficients”, Electronics & Communications in Japan, Part III: Fundamental Electronic Science, vol. 85, no. 3, pp. 52–60, 2002. https://doi.org/10.1002/ecjc.1079
E. Watanabe and A. Nishihara, “A synthesis of a class of complex digital filters based on circuitry transformations”. IEICE Trans., vol. E-74, no. 11, pp. 3622–3624, Nov. 1991.
G. Stoyanov, M. Kavamata, and Z. Valkova. “New First and Second-Order Very Low-Sensitivity Bandpass/Bandstop Complex Digital Filter Sections”, Proc. IEEE 1997 Region 10th Annual Conf., TENCON’97, Brisbane, Australia, vol. 1, pp. 61–64, Dec. 2–4, 1997.
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Copyright (c) 2020 Zlatka Valkova-Jarvis et al., published by Sciendo
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Valkova-Jarvis, Z., Mihaylova, D., & Stoynov, V. (2020). Efficient Orthogonal Bicomplex Bilinear DSP Algorithm Design. Electrical, Control and Communication Engineering, 16(1), 30-36. https://doi.org/10.2478/ecce-2020-0005
