Even mirror Fourier nonlinear filters

In this paper, a novel sub-class of linear-in-the-parameters (LIP) nonlinear filters, formed by the so-called even mirror Fourier nonlinear (EMFN) filters, is presented. These filters are universal approximators for causal, time invariant, finite-memory, continuous nonlinear systems as the well-known Volterra filters. However, in contrast to Volterra filters, their basis functions are mutually orthogonal for white uniform input signals. Therefore, in adaptive applications, gradient descent algorithms with fast convergence speed and efficient nonlinear system identification algorithms can be devised. Preliminary results, showing the potentialities of EMFN filters in comparison with other LIP nonlinear filters, are presented and commented.

[1]  Jagdish C. Patra,et al.  A functional link artificial neural network for adaptive channel equalization , 1995, Signal Process..

[2]  Jungsang Kim,et al.  Digital predistortion of wideband signals based on power amplifier model with memory , 2001 .

[3]  Martin D. Buhmann,et al.  Radial Basis Functions: Theory and Implementations: Preface , 2003 .

[4]  Rui Seara,et al.  A Sparse-Interpolated Scheme for Implementing Adaptive Volterra Filters , 2010, IEEE Transactions on Signal Processing.

[5]  Yoh-Han Pao,et al.  Adaptive pattern recognition and neural networks , 1989 .

[6]  G. Sicuranza,et al.  On the Accuracy of Generalized Hammerstein Models for Nonlinear Active Noise Control , 2006, 2006 IEEE Instrumentation and Measurement Technology Conference Proceedings.

[7]  George-Othon Glentis,et al.  Efficient algorithms for Volterra system identification , 1999, IEEE Trans. Signal Process..

[8]  Giovanni L. Sicuranza,et al.  Piecewise-Linear Expansions for Nonlinear Active Noise Control , 2006, 2006 IEEE International Conference on Acoustics Speech and Signal Processing Proceedings.

[9]  Giovanni L. Sicuranza,et al.  Recursive controllers for nonlinear active noise control , 2011, 2011 7th International Symposium on Image and Signal Processing and Analysis (ISPA).

[10]  Xiangping Zeng,et al.  Adaptive reduced feedback FLNN filter for active control of nonlinear noise processes , 2010, Signal Process..

[11]  Walter Kellermann,et al.  Partitioned block frequency-domain adaptive second-order Volterra filter , 2005, IEEE Transactions on Signal Processing.

[12]  J. Arenas-García,et al.  Functional link based architectures for nonlinear acoustic echo cancellation , 2011, 2011 Joint Workshop on Hands-free Speech Communication and Microphone Arrays.

[13]  Giovanni L. Sicuranza,et al.  Adaptive recursive FLANN filters for nonlinear active noise control , 2011, 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[14]  Giovanni L. Sicuranza,et al.  On the BIBO Stability Condition of Adaptive Recursive FLANN Filters With Application to Nonlinear Active Noise Control , 2012, IEEE Transactions on Audio, Speech, and Language Processing.

[15]  V. John Mathews,et al.  A stable adaptive Hammerstein filter employing partial orthogonalization of the input signals , 2002, IEEE Transactions on Signal Processing.

[16]  V. John Mathews,et al.  Stochastic mean-square performance analysis of an adaptive Hammerstein filter , 2006, IEEE Transactions on Signal Processing.

[17]  Ganapati Panda,et al.  Active mitigation of nonlinear noise Processes using a novel filtered-s LMS algorithm , 2004, IEEE Transactions on Speech and Audio Processing.

[18]  Tariq S. Durrani,et al.  Theory and applications of adaptive second order IIR Volterra filters , 1996, 1996 IEEE International Conference on Acoustics, Speech, and Signal Processing Conference Proceedings.

[19]  Rui Seara,et al.  A fully LMS adaptive interpolated Volterra structure , 2008, 2008 IEEE International Conference on Acoustics, Speech and Signal Processing.

[20]  Li Tan,et al.  Adaptive Volterra filters for active control of nonlinear noise processes , 2001, IEEE Trans. Signal Process..

[21]  Jaehyeong Kim,et al.  A Generalized Memory Polynomial Model for Digital Predistortion of RF Power Amplifiers , 2006, IEEE Transactions on Signal Processing.

[22]  Giovanni L. Sicuranza,et al.  Efficient NLMS and RLS algorithms for a class of nonlinear filters using periodic input sequences , 2011, 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[23]  V. J. Mathews,et al.  Polynomial Signal Processing , 2000 .

[24]  W. Rudin.  Principles of mathematical analysis , 1964 .

[25]  Aníbal R. Figueiras-Vidal,et al.  Adaptive Combination of Volterra Kernels and Its Application to Nonlinear Acoustic Echo Cancellation , 2011, IEEE Transactions on Audio, Speech, and Language Processing.

[26]  G. L. Sicuranza,et al.  A Generalized FLANN Filter for Nonlinear Active Noise Control , 2011, IEEE Transactions on Audio, Speech, and Language Processing.

[27]  Dayong Zhou,et al.  Efficient Adaptive Nonlinear Filters for Nonlinear Active Noise Control , 2007, IEEE Transactions on Circuits and Systems I: Regular Papers.

[28]  Walter Kellermann,et al.  Online estimation of the optimum quadratic kernel size of second-order Volterra filters using a convex combination scheme , 2009, 2009 IEEE International Conference on Acoustics, Speech and Signal Processing.