Determining the Weights of A Fourier Series Neural Network on the Basis of the Multidimensional Discrete Fourier Transform

Bracewell R. (1999). The Fourier Transform and Its Applications, 3rd Edn., McGraw-Hill, New York, NY.Search in Google Scholar

Chu E. and George A. (2000). Inside the FFT Black Box: Serial and Parallel Fast Fourier Transform Algorithms, CRC Press, Boca Raton, FL.10.1201/9781420049961Search in Google Scholar

Dutt A. and Rokhlin V. (1993). Fast Fourier transforms for nonequispaced data, Journal of Scientific Computing14(6): 1368-1393.10.1137/0914081Search in Google Scholar

Gonzalez R. C. and Woods R. E. (1999). Digital Image Processing, 2nd Edn., Prentice-Hall, Inc., Boston, MA.Search in Google Scholar

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).Search in Google Scholar

Hyvarinen A. and Oja E. (2000). Independent component analysis: Algorithms and applications, Neural Networks13(4): 411-430.10.1016/S0893-6080(00)00026-5Search in Google Scholar

Joliffe I. T. (1986). Principal Component Analysis, Springer-Verlag, New York, NY.10.1007/978-1-4757-1904-8Search in Google Scholar

Kegl B., Krzyżak A., Linder T. and Zeger K. (2000). Learning and design of principal curves, IEEE Transactions on Pattern Analysis and Machine Intelligence22(13): 281-297.10.1109/34.841759Search in Google Scholar

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.Search in Google Scholar

Liu Q. H. and Nyguen N. (1998). An accurate algorithm for nonuniform fast Fourier transforms, Microwave and Guided Wave Letters8(1): 18-20.10.1109/75.650975Search in Google Scholar

Nelles O. (2001). Nonlinear System Identification: From Classical Approaches to Neural Network and Fuzzy Models, Springer-Verlag, Berlin.Search in Google Scholar

Rafajłowicz E. and Pawlak M. (1997). On function recovery by neural networks based on orthogonal expansions, Nonlinear Analysis, Theory and Applications30(3): 1343-1354.10.1016/S0362-546X(97)00223-XSearch in Google Scholar

Rafajłowicz E. and Skubalska-Rafajłowicz E. (1993). FFT in calculating nonparametric regression estimate based on trigonometric series, International Journal of Applied Mathematics and Computer Science3(4): 713-720.Search in Google Scholar

Sher C. F., Tseng C. S. and Chen C. (2001). Properties and performance of orthogonal neural network in function approximation, International Journal of Intelligent Systems16(12): 1377-1392.10.1002/int.1065Search in Google Scholar

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 Systems19(12): 1257-1275.10.1002/int.20047Search in Google Scholar

Van Loan C. (1992). Computational Frameworks for the Fast Fourier Transform, SIAM, Philadelphia, PA.10.1137/1.9781611970999Search in Google Scholar

Walker J. (1996). Fast Fourier Transforms, CRC Press, Boca Raton, FL.Search in Google Scholar

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.Search in Google Scholar