Adaptive Matrix/Vector Gradient Algorithm for Design of IIR Filters and ARMA Models


This work describes a novel adaptive matrix/vector gradient (AMVG) algorithm for design of IIR filters and ARMA signal models. The AMVG algorithm can track to IIR filters and ARMA systems having poles also outside the unit circle. The time reversed filtering procedure was used to treat the unstable conditions. The SVD-based null space solution was used for the initialization of the AMVG algorithm. We demonstrate the feasibility of the method by designing a digital phase shifter, which adapts to complex frequency carriers in the presence of noise. We implement the half-sample delay filter and describe the envelope detector based on the Hilbert transform filter.

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J. Olkkonen, S. Ahtiainen, K. Jarvinen and H. Olkkonen, "Adaptive Matrix/Vector Gradient Algorithm for Design of IIR Filters and ARMA Models," Journal of Signal and Information Processing, Vol. 4 No. 2, 2013, pp. 212-217. doi: 10.4236/jsip.2013.42028.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] J. T. Olkkonen, “Discrete Wavelet Transforms: Theory and Applications,” Intech, 2011.
[2] H. Olkkonen, “Discrete Wavelet Transforms: Algorithms and Applications,” Intech, 2011, 296 p.
[3] H. Olkkonen, “Discrete Wavelet Transforms: Biomedical Applications,” Intech, 2011, 366 p.
[4] J. T. Olkkonen and H. Olkkonen, “Fractional Delay Filter Based on the B-Spline Transform,” IEEE Signal Processing Letters, Vol. 14, No. 2, 2007, pp. 97-100. doi:10.1109/LSP.2006.882103
[5] H. Olkkonen, S. Ahtiainen, J. T. Olkkonen and P. Pesola, “State-Space Modelling of Dynamic Systems Using Hankel Matrix Representation,” International Journal of Computer Science & Emerging Technologies, Vol. 1, No. 4, 2010, pp. 112-115.
[6] J. T. Olkkonen and H. Olkkonen, “Least Squares Matrix Algorithm for State-Space Modelling of Dynamic Systems,” Journal of Signal and Information Processing, Vol. 2, No. 4, 2011, pp. 287-291. doi:10.4236/jsip.2011.24041
[7] H. Olkkonen and J. T. Olkkonen, “Shift-Invariant B-Spline Wavelet Transform for Multi-Scale Analysis of Neuroelectric Signals,” IET Signal Processing, Vol. 4, No. 6, 2010, pp. 603-609. doi:10.1049/iet-spr.2009.0109
[8] J. T. Olkkonen and H. Olkkonen, “Complex Hilbert Transform Filter,” Journal of Signal and Information Processing, Vol. 2, No. 2, 2011, pp. 112-116.
[9] F. Daum, “Nonlinear Filters: Beyond the Kalman Filter,” IEEE A&E Systems Magazine, Vol. 20, No. 8, 2005, pp. 57-69.
[10] A. Moghaddamjoo and R. Lynn Kirlin, “Robust Adaptive Kalman Filtering with Unknown Inputs,” IEEE Transactions on Acoustics, Speech and Signal Processing, Vol. 37, No. 8, 1989, pp. 1166-1175. doi:10.1109/29.31265
[11] J. L. Maryak, J. C. Spall and B. D. Heydon, “Use of the Kalman Filter for Interference in State-Space Models with Unknown Noise Distributions,” IEEE Transactions on Automatic Control, Vol. 49, No. 1, 2005, pp. 87-90.
[12] R. Diversi, R. Guidorzi and U. Soverini, “Kalman Filtering in Extended Noise Environments,” IEEE Transactions on Automatic Control, Vol. 50, No. 9, 2005, pp. 1396-1402. doi:10.1109/T AC.2005.854627
[13] D.-J. Jwo and S.-H. Wang, “Adaptive Fuzzy Strong Tracking Extended Kalman Filtering for GPS Navigation,” IEEE Sensors Journal, Vol. 7, No. 5, 2007, pp. 778-789. doi:10.1109/JSEN.2007.894148
[14] S. Attallah, “The Wavelet Transform-Domain LMS Adaptive Filter with Partial Subband-Coefficient Updating,” IEEE Transactions on Circuits and Systems II, Vol. 53, No. 1, 2006, pp. 8-12. doi:10.1109/TCSII.2005.855042
[15] H. Olkkonen, P. Pesola, A. Valjakka and L. Tuomisto, “Gain Optimized Cosine Transform Domain LMS Algorithm for Adaptive Filtering of EEG,” Computers in Biology and Medicine, Vol. 29, No. 2, 1999, pp. 129-136. doi:10.1016/S0010-4825(98)00046-8
[16] E. Biglieri and K. Yao, “Some Properties of Singular Value Decomposition and Their Applications to Digital Signal Processing,” Signal Processing, Vol. 18, No. 3, 1989, pp. 277-289. doi:10.1016/0165-1684(89)90039-X
[17] S. Park, T. K. Sarkar and Y. Hua, “A Singular Value Decomposition-Based Method for Solving a Deterministic Adaptive Problem,” Digital Signal Processing, Vol. 9, No. 1, 1999, pp. 57-63. doi:10.1006/dspr.1998.0331
[18] T. J. Willink, “Efficient Adaptive SVD Algorithm for MIMO Applications,” IEEE Transactions on Signal Processing, Vol. 56, No. 2, 2008, pp. 615-622. doi:10.1109/TSP.2007.907806
[19] T. J. Lim and M. D. Macleaod, “On Line Interpolation Using Spline Functions,” IEEE Signal Processing Society, Vol. 3, No. 5, 1996, pp. 144-146. doi:10.1109/97.491656
[20] J. T. Olkkonen and H. Olkkonen, “Fractional Time-Shift BSpline Filter,” IEEE Signal Processing Letters, Vol. 14, No. 10, 2007, pp. 688-691. doi:10.1109/LSP.2007.896402
[21] J. T. Olkkonen and H. Olkkonen, “Shift Invariant Biorthogonal Discrete Wavelet Transform for EEG Signal Analysis, Book Chapter 9,” In: J. T. Olkkonen, Ed., Discrete Wavelet Transforms: Theory and Applications, Intech, 2011. doi:10.5772/23828
[22] J. T. Olkkonen and H. Olkkonen, “Discrete Wavelet Transform Algorithms for Multi-Scale Analysis of Biomedical Signals, Book Chapter 4,” In: H. Olkkonen, Ed., Discrete Wavelet Transforms: Biomedical Applications, Intech, 2011.

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