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waveforms using knowledge of channel coherence[C] // Oceans. IEEE, 2010:1-8. 5. PING Xian-jun Tao-ran ZHOU Si-yong. A new fast algorithm of fractional Fourier transform [J]. Electronic journal, 2001,29 (3): 406-408 6. Wang Juan-feng. Research on digital watermarking algorithm based on fractional Fourier domain image features.[D] Zhengzhou University, 2007 7. Bultheel A, Sulbaran H E M. Computation of the fractional Fourier transform[J]. Applied & Computational Harmonic Analysis, 2004,16(3):182-202. 8. Cheng Xue. Digital watermarking technology based on fractional Fourier

indykatorowego , Laboratorium Silników spalinowych – Materiały pomocnicze, Katedra Silników Spalinowych i Transportu, Politechnika Rzeszowska. [6] http://mathworld.wolfram.com/FourierTransform.html . [7] http://mathworld.wolfram.com/DiscreteFourierTransform.html . [8] http://mathworld.wolfram.com/FastFourierTransform.html . [9] https://www.dataq.com/data-acquisition/general-education-tutorials/fft-fast-fourier-transform-waveform-analysis.html . [10] Jankowski, A., Chosen Problems of Combustion Processes of Advanced Combustion Engine , Journal of KONES, Vol. 20, No. 3, DOI

References Attari, M. (2004). Option pricing using Fourier transforms: A numerically efficient simplification. Retrieved from http://papers.ssrn.com/sol3/papers.cfm?abstract_id=520042. doi: 10.2139/ssrn.520042 Bakshi, G., & Madan, D. (2000). Spanning and derivative - security valuation. Journal of Financial Economics, 55(2), 205-238. doi: 10.1016/S0304-405X(99)00050-1 Bates, D. (2006). Maximum likelihood estimation of latent affine processes. Review of Financial Studies, 19(3), 909-965. doi: 10.1093/rfs/hh Black, F., & Scholes, M. (1973). The pricing of

, Reihe A — Theoretische Geodäsie, Heft 119, Verlag der Bayerischen Akademie der Wissenschaften, München. Fabert O., Schmidt M. (2003) Wavelet Filtering with High Time-Frequency Resolution and Effective Numerical Implementation Applied on Polar Motion, Artificial Satellites — Journal of Planetary Geodesy , Vol. 38, No. 1, 3-13. Forbes A.M.G. (1988) Fourier Transform Filtering: A Cautionary Note, Journal of Geophysical Research , Vol. 93, No. C6, 6958-6962. Gasquet C., Witomski P. (1999) Fourier Analysis and Applications — Filtering, Numerical Computation, Wavelets

Motion, Artificial Satellites - Journal of Planetary Geodesy , Vol. 38, No. 1, 3-13. Ferreira P.J.S.G., and Kempf A. (2006) Superoscillations: Faster Than the Nyquist Rate, IEEE Transactions on Signal Processing , Vol. 54, No. 10, 3732-3740. Forbes A.M.G. (1988) Fourier Transform Filtering: A Cautionary Note, Journal of Geophysical Research , Vol. 93, No. C6, 6958-6962. Gasquet C., Witomski P. (1999) Fourier Analysis and Applications - Filtering, Numerical Computation, Wavelets , Springer Verlag Inc., New York. Hasan T. (1983) Complex Demodulation: Some Theory and

., 18 (2) (2013), 260-273. [9] R. Khalil, M. Al Horani, A. Yousef, M. Sababheh, A new definition of fractional derivative, J. Comput. Appl. Math., 264 (2014), 65-70. [10] M. Abu Hammad, R. Khalil, Conformable fractional heat differential equation, Int. J. Pure Appl. Math., 94 (2) (2014), 215-221. [11] P. K. Kythe, P. Puri, M. R. Schäferkotter, Partial Differential Equations and Mathematica, CRC Press, 1997. [12] T. Abdeljawad, On conformable fractional calculus, J. Comput. Appl. Math., 279 (2015) 57-66. [13] N. T. Negero, Fourier transform methods for partial

References Bracewell R. (1999). The Fourier Transform and Its Applications, 3rd Edn. , McGraw-Hill, New York, NY. Chu E. and George A. (2000). Inside the FFT Black Box: Serial and Parallel Fast Fourier Transform Algorithms , CRC Press, Boca Raton, FL. Dutt A. and Rokhlin V. (1993). Fast Fourier transforms for nonequispaced data, Journal of Scientific Computing 14 (6): 1368-1393. Gonzalez R. C. and Woods R. E. (1999). Digital Image Processing, 2nd Edn. , Prentice-Hall, Inc., Boston, MA. Halawa K. (2008). Fast method for computing outputs of Fourier neutral

Abstract

The article proposes a method of mathematical simulation of electrical machines with thyristor exciters on the basis of the local Fourier transform. The present research demonstrates that this method allows switching from a variable structure model to a constant structure model. Transition from the continuous variables to the discrete variables is used. The numerical example is given in the paper.

, 1213-1227. Cited on 121. [9] G.H. Hardy, Note on a theorem of Hilbert, Math. Z. 6 (1920), no. 3-4, 314-317. Cited on 122. [10] G.H. Hardy, J.E. Littlewood, G. Pólya, Inequalities, 2d ed., Cambridge University Press, 1952. Cited on 127. [11] H.P. Heinig, Weighted norm inequalities for classes of operators, Indiana Univ. Math. J. 33 (1984), no. 4, 573-582. Cited on 127. [12] M. Jr. Jodeit, A. Torchinsky, Inequalities for Fourier transforms, Studia Math. 37 (1970/71), 245-276. Cited on 126. [13] V.G. Maz’ja, Sobolev spaces, Springer Series in Soviet Mathematics

Fourier Transform. in 2014 IEEE Radar Conference, Cincinnati, Ohio, 19-23 May 2014. 12. F. Zhang, R. Tao, Y. Wang.: Angle Resolution of Fractional Fourier Transform. 2014 31th URSI General Assembly and Scientific Symposium, URSI GASS 2014, October 17, 2014 13. Zhang. Lili, Liu Sixin, Qu, Lete, et al.: Research on wavelet extraction of gpr signals based on multilevel fractional fourier transform filter [J]. Journal of the Balkan Tribological Assocaitaion, Vol. 22, No 1, 2016, p. 807-818 14. H.M. Ozaktas, M.A. Kutay, D. Mendlovic.: Introduction to the Fractional Fourier