Fuzzy Digital Filtering: Signal Interpretation

Juan C. García Infante, J. Jesús Medel Juárez, Juan C. Sánchez García

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DOI: 10.4236/ijcns.2011.45034                

Abstract

The paper makes a description of the fuzzy filter properties considering its operational principles. A digital filter interacts with a reference model signal into real process in order to get the best corresponding answer, having the minimum error at the filter output using the mean square criterion. Adding into this filter structure a fuzzy mechanism, to obtain an intelligent filtering because adaptively select and emit a decision answer according with the external reference signal changes, in order to actualize the best correct new conditions updating a process dynamically. The interpretation of the input signal level describes the operation of the reference model, to update the filter weights giving the answers approximation in accordance with the reference signal in natural form. Finally the paper shows the simulations results of the fuzzy filter into the Kalman structure using the Matlab© tool.

Keywords

Digital Filters, Fuzzy Systems, Signal Processing, Estimation, Probability

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	B. Rajen and M. Gopal, “Neuro-Fuzzy Decision Trees,” International Journal of Neural Filters, Vol. 16, No. 1, 2006, pp. 63-68. doi:10.1142/S0129065706000470
[2]	K. M. Passino, “Fuzzy Control,” Addison Wesley, Boston, 1998.
[3]	M. Margaliot and G. Langholz, “New Approaches to Fuzzy Modeling and Control Design and Analysis,” World Scientific, Singapore, 2000. doi:10.1142/9789812792716
[4]	S. Haykin, “Adaptive Filtering,” Prentice Hall, Upper Saddle River, 2001.
[5]	T. Yamakawa, “A Survey on Fuzzy Information Processing Hardware Systems,” 1995 IEEE International Symposium on Circuits and Systems, Seattle, 28 April - 5 March 1995, pp. 1310-1314.
[6]	J. J. Medel, J. C. García and J. C. Sánchez, “Real-Time Fuzzy Digital Filters Properties for SISO Systems,” Automatic Control and Computer Sciences, Vol. 41, No. 1, 2008, pp. 26-34.
[7]	S. Mollov, R. Babuska, J. Abonyi, and H. Verbruggen, “Effective Optimization for Fuzzy Model Predictive Control,” IEEE Transactions on Fuzzy Systems, Vol. 12, No. 5, 2004, pp. 661-675. doi:10.1109/TFUZZ.2004.834812
[8]	R. Ash, “Real Analysis and Probability,” Academic Press, Cambridge, 1970.
[9]	L. Zadeh, “Maximizing Sets and Fuzzy Markoff Algorithms,” IEEE Transactions on Systems, Man, and Cybernetics-Part C: Applications and Reviews, Vol. 28, No. 1, 1998, pp. 9-15. doi:10.1109/5326.661086
[10]	G. Feng, “A Survey on Analysis and Desing of Model- Based Fuzzy Control Systems,” IEEE Transactions on Fuzzy Systems, Vol. 14, No. 5, 2006, pp. 676-697. doi:10.1109/TFUZZ.2006.883415
[11]	J. García, J. Medel and L. Guevara, “Filtrado Difuso en Tiempo Real,” Computación y Sistemas, Vol. 11, No. 4, 2008, pp. 390-401.
[12]	J. García, J. Medel and J. Sánchez, “Evolutive Neural Net Fuzzy Filtering: Basic Description,” Journal of Intelligent Learning Systems and Applications, Vol. 2, No. 1, 2010, pp. 12-18. doi:10.4236/jilsa.2010.21002
[13]	B. Kosko, “Fuzzy Engineering,” Prentice Hall, Upper Saddle River, 1997.
[14]	E. Mamdani, “Applications of Fuzzy Algorithms for Control of Simple Dynamic Plant,” Proceedings of IEEE, Vol. 121, No. 12, 1974, pp. 1585-1588.
[15]	T. Amble, “Logic Programming and Knowledge Engineering,” Addison Wesley, Boston, 1987.
[16]	T. Takagi and M. Sugeno, “Fuzzy Identification of Systems and Its Applications to Modelling and Control,” IEEE Transactions and Systems, Man, and Cybernetics, Vol. 15, No. 1, 1985, pp. 116-132.
[17]	M. Shannon, “A Mathematical Theory of Communication,” Bell Systems Technical Journal, Vol. 27, 1948, pp. 379-423 and pp. 623-656.
[18]	J. Smith and A. Eiben, “Introduction to Evolutionary Computing,” Springer, Cambridge, 2003.
[19]	L. Zadeh, “Fuzzy Sets,” Information and Control, Vol. 8, No. 3, 1965, pp. 338-353. doi:10.1016/S0019-9958(65)90241-X
[20]	H. S. Ali, “Fundamentals of Adaptive Filters,” John Wiley & Sons, Hoboken, 2003.
[21]	E. Onieva, V. Milanés, J. Pérez and T. Pedro, “Estima- ción de un Control Lateral Difuso de Vehículos,” Inicio, Vol. 7, No. 2, 2010, pp. 91-98.
[22]	D. Marcek, “Stock Price Forecasting: Statistical, Classi- cal and Fuzzy Neural Networks,” The 8th International Conference on Modeling Decisions for Artificial Intelligence, Barcelona, 2-4 August 2004, pp. 41-48.
[23]	F. Gustafsson, “Adaptive Filtering and Change Detec- tion,”John Wiley and Sons, Ltd., Hoboken, 2000. doi:10.1002/0470841613