A Novel Adaptive Nonlinear Filter-Based Pipelined Feedforward Second-Order Volterra Architecture

Due to the computational complexity of the Volterra filter, there are limitations on the implementation in practice. In this paper, a novel adaptive joint process filter using pipelined feedforward second-order Volterra architecture (JPPSOV) to reduce the computational burdens of the Volterra filter is proposed. The proposed architecture consists of two subsections: nonlinear subsection performing a nonlinear mapping from the input space to an intermediate space by the feedforward second-order Volterra (SOV), and a linear combiner performing a linear mapping from the intermediate space to the output space. The corresponding adaptive algorithms are deduced for the nonlinear and linear combiner subsections, respectively. Moreover, the analysis of theory shows that these adaptive algorithms based on the pipelined architecture are stable and convergence under a certain condition. To evaluate the performance of the JPPSOV, a series of simulation experiments are presented including nonlinear system identification and predicting of speech signals. Compared with the conventional SOV filter, adaptive JPPSOV filter exhibits a litter better convergence performance with less computational burden in terms of convergence speed and steady-state error.

[1]  Jonathon A. Chambers,et al.  Nonlinear adaptive prediction of speech with a pipelined recurrent neural network , 1998, IEEE Trans. Signal Process..

[2]  P. Chang,et al.  Narrow-band interference suppression in spread-spectrum CDMA communications using pipelined recurrent neural networks , 1999 .

[3]  V. John Mathews,et al.  Parallel-cascade realizations and approximations of truncated Volterra systems , 1998, IEEE Trans. Signal Process..

[4]  Mohammad M. Banat.  Pipelined Volterra filter , 1992 .

[5]  Danilo P. Mandic,et al.  Recurrent Neural Networks for Prediction: Learning Algorithms, Architectures and Stability , 2001 .

[6]  Walter A. Frank.  An efficient approximation to the quadratic Volterra filter and its application in real-time loudspeaker linearization , 1995, Signal Process..

[7]  Liang Li,et al.  Nonlinear adaptive prediction of nonstationary signals , 1995, IEEE Trans. Signal Process..

[8]  Giovanni L. Sicuranza,et al.  On reduced-complexity approximations of quadratic filters , 1993, Proceedings of 27th Asilomar Conference on Signals, Systems and Computers.

[9]  Giovanni L. Sicuranza,et al.  Adaptive parallel-cascade truncated Volterra filters , 1998, IEEE Trans. Signal Process..

[10]  Jianming Lu,et al.  A Method for Parallel Adaptive Volterra Filter Using RLS Algorithm , 2006 .

[11]  Mo Chen,et al.  An Assessment of Qualitative Performance of Machine Learning Architectures: Modular Feedback Networks , 2008, IEEE Transactions on Neural Networks.

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

[13]  Bernard Mulgrew,et al.  Nonlinear system identification and prediction using orthogonal functions , 1997, IEEE Trans. Signal Process..

[14]  V. J. Mathews,et al.  Efficient block-adaptive parallel-cascade quadratic filters , 1999 .

[15]  Richard D. Braatz,et al.  On the "Identification and control of dynamical systems using neural networks" , 1997, IEEE Trans. Neural Networks.

[16]  Chrysostomos L. Nikias,et al.  Efficient VLSI array processing structures for adaptive quadratic digital filters , 1988 .

[17]  Takao Hinamoto,et al.  A pipeline architecture of quadratic adaptive Volterra filters based on NLMS algorithm , 2001, ISCAS 2001. The 2001 IEEE International Symposium on Circuits and Systems (Cat. No.01CH37196).

[18]  S. Haykin,et al.  Adaptive Filter Theory , 1986 .

[19]  V. J. O H N M A T H.  Adaptive Polynomial Filters , 2022 .

[20]  G. Sicuranza.  Quadratic filters for signal processing , 1992, Proc. IEEE.

[21]  S. Haykin,et al.  A cascaded recurrent neural network for real-time nonlinear adaptive filtering , 1993, IEEE International Conference on Neural Networks.

[22]  H. Grady Rylander,et al.  A second-order adaptive Volterra filter with rapid convergence , 1987, IEEE Trans. Acoust. Speech Signal Process..

[23]  Danilo P. Mandic,et al.  Nonlinear adaptive prediction of complex-valued signals by complex-valued PRNN , 2005, IEEE Transactions on Signal Processing.

[24]  Danilo P. Mandic,et al.  Recurrent Neural Networks for Prediction: Learning Algorithms, Architectures and Stability , 2001 .

[25]  Taiho Koh,et al.  Second-order Volterra filtering and its application to nonlinear system identification , 1985, IEEE Trans. Acoust. Speech Signal Process..

[26]  G. Sicuranza,et al.  Nonlinear digital filter realization by distributed arithmetic , 1985, IEEE Trans. Acoust. Speech Signal Process..

[27]  M. Schetzen.  The Volterra and Wiener Theories of Nonlinear Systems , 1980 .

[28]  Jianming Lu,et al.  A design method for parallel recursive least square adaptive Volterra filter , 2005, 2005 IEEE International Symposium on Circuits and Systems.

[29]  M. Schetzen,et al.  Nonlinear system modeling based on the Wiener theory , 1981, Proceedings of the IEEE.