Determining the weights of a Fourier series neural network on the basis of the multidimensional discrete Fourier transform

• Autorzy: Halawa K.
• Języki publikacji: EN

Abstrakty

EN

This paper presents a method for training a Fourier series neural network on the basis of the multidimensional discrete Fourier transform. The proposed method is characterized by low computational complexity. The article shows how the method can be used for modelling dynamic systems.

Słowa kluczowe

EN

orthogonal neural networks; Fourier series; fast Fourier transform; approximation; nonlinear system

PL

sieć neuronowa ortogonalna; szereg Fouriera; transformata Fouriera; aproksymacja; system nieliniowy

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2008
• Tom: Vol. 18, no 3
• Strony: 369--375
• Opis fizyczny: Bibliogr. 18 poz., rys., wykr.

Twórcy

autor

Halawa K.

• Institute of Computer Engineering, Control and Robotics, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50–370 Wroclaw, Poland,

Bibliografia

• [1] Bracewell R. (1999). The Fourier Transform and Its Applications, 3rd Edn., McGraw-Hill, New York, NY.
• [2] Chu E. and George A. (2000). Inside the FFT Black Box: Serial and Parallel Fast Fourier Transform Algorithms, CRC Press, Boca Raton, FL.
• [3] Dutt A. and Rokhlin V. (1993). Fast Fourier transforms for nonequispaced data, Journal of Scientific Computing 14(6): 1368-1393.
• [4] Gonzalez R. C. and Woods R. E. (1999). Digital Image Processing, 2nd Edn., Prentice-Hall, Inc., Boston, MA.
• [5] Halawa K. (2008). Fast method for computing outputs of Fourier neutral networks, in: K. Malinowski and L. Rutkowski, Eds., Control and Automation: Current Problems and Their Solutions, EXIT, Warsaw, pp. 652-659, (in Polish).
• [6] Hyvarinen A. and Oja E. (2000). Independent component analysis: Algorithms and applications, Neural Networks 13(4): 411-430.
• [7] Joliffe I. T. (1986). Principal Component Analysis, Springer-Verlag, New York, NY.
• [8] Kegl B., Krzy˙zak A., Linder T. and Zeger K. (2000). Learning and design of principal curves, IEEE Transactions on Pattern Analysis and Machine Intelligence 22(13): 281-297.
• [9] Li H. and Sun Y. (2005). The study and test of ICA algorithms, Proceedings of the International Conference on Wireless Communications, Networking and Mobile Computing, Wuhan, China, pp. 602-605.
• [10] Liu Q. H. and Nyguen N. (1998). An accurate algorithm for nonuniform fast Fourier transforms, Microwave and Guided Wave Letters 8(1): 18-20.
• [11] Nelles O. (2001). Nonlinear System Identification: From Classical Approaches to Neural Network and Fuzzy Models Springer-Verlag, Berlin.
• [12] Rafajłowicz E. and Pawlak M. (1997). On function recovery by neural networks based on orthogonal expansions, Nonlinear Analysis, Theory and Applications 30(3): 1343-1354.
• [13] Rafajłowicz E. and Skubalska-Rafajłowicz E. (1993). FFT in calculating nonparametric regression estimate based on trigonometric series, International Journal of Applied Mathematics and Computer Science 3(4): 713-720.
• [14] Sher C. F., Tseng C. S. and Chen, C. (2001). Properties and performance of orthogonal neural network in function approximation, International Journal of Intelligent Systems 16(12): 1377-1392.
• [15] Tseng C. S. and Chen C. S. (2004). Performance comparison between the training method and the numerical method of the orthogonal neural network in function approximation, International Journal of Intelligent Systems 19(12): 1257-1275.
• [16] Van Loan C. (1992). Computational Frameworks for the Fast Fourier Transform, SIAM, Philadelphia, PA.
• [17] Walker J. (1996). Fast Fourier Transforms, CRC Press, Boca Raton, FL.
• [18] Zhu C., Shukla D. and Paul, F. (2002). Orthogonal functions for system identification and control, in: C.T. Leondes (Ed.), Neural Networks Systems, Techniques and Apllications: Control and Dynamic Systems, Academic Press, San Diego, CA, pp. 1-73.