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Design of IIR all-pass filters using a neural-based learning algorithm. (English) Zbl 1358.94022
Summary: Least-squares design of infinite impulse response all-pass filter can be formulated as an eigenvector solving problem based on the Rayleigh principle. The eigenfilter is designed by solving a single eigenvector corresponding to the smallest eigenvalue of a real, symmetric, and positive-definite matrix. This paper proposes a minor component analysis-based neural learning algorithm for designing eigenfilter. By appropriately mapping the associated all-pass filter specifications to the simple neural model enables the filter coefficients to be derived from the neural weights. The neural weights eventually approach the optimal filter coefficients of the eigenfilter when the neural model achieves convergence. The proposed neural learning algorithm is demonstrated from simulation results to converge rapidly and achieve accurate performance of eigenfilter design.
94A12 Signal theory (characterization, reconstruction, filtering, etc.)
68T05 Learning and adaptive systems in artificial intelligence
Full Text: DOI
[1] Chan, SC; Chen, HH; Pun, Carson KS, The design of digital all-pass filters using second-order cone programming (SOCP), IEEE Trans. Circuits Syst. II Express Briefs, 52, 66-70, (2005)
[2] Chen, CK; Lee, JH, Design of digital all-pass filters using a weighted least squares approach, IEEE Trans. Circuits Syst. II Analog Digit. Signal Process., 41, 346-351, (1994)
[3] L.W. Chen, Y.D. Jou, F.K. Chen, S.S. Hao, Eigenfilter design of linear-phase FIR digital filters using neural minor component analysis. Digit. Signal Process. 32, 146-155 (2014)
[4] L.W. Chen, J.K. Huang, Y.D. Jou, S.S. Hao, IIR all-pass filters design based on neural learning algorithm. in 2014 IEEE International Symposium on Computer, Consumer and Control (2014) pp. 1233-1236
[5] Fiori, S, Neural minor component analysis approach to robust constrained beamforming, IEE Proc. Vis. Image Signal Process., 150, 205-218, (2003)
[6] M. Ikehara, M. Funaishi, H. Kuroda, Design of all-pass networks using Remez algorithm. in Proc. IEEE International Symposium Circuits and Systems (1991), pp. 364-367 · Zbl 0775.93257
[7] Ikehara, M; Funaishi, M; Kuroda, H, Design of complex all-pass networks using Remez algorithm, IEEE Trans. Circuits Syst. II Analog Digit. Signal Process., 39, 549-556, (1992) · Zbl 0775.93257
[8] Jiang, A; Kwan, HK, IIR digital filter design with new stability constraint based on argument principle, IEEE Trans. Circuits Syst. I Regul. Pap., 56, 583-593, (2009)
[9] Jing, Z, A new method for digital all-pass filter design, IEEE Trans. Acoust. Speech Signal Process., 35, 1557-1564, (1987)
[10] Y.D. Jou, F.K. Chen, Design of Hilbert transformer and digital differentiator using a neural learning algorithm. in 2012 IEEE International Symposium on Intelligent Signal Processing and Communications System (2012), pp. 380-384
[11] Y.D. Jou, F.K. Chen, L.C. Su, C.M. Sun, Weighted least-squares design of IIR all-pass filters using a Lyapunov error criterion. in 2010 IEEE Asia-Pacific Conference on Circuits and Systems (2010), pp. 1071-1074
[12] Y.D. Jou, F.K. Chen, C.M. Sun, Eigenfilter design of FIR digital filters using minor component analysis. in 2013 International Conference on Information, Communications and Signal Processing (2013)
[13] Kidambi, SS, Weighted least-squares design of recursive all-pass filters, IEEE Trans. Signal Process., 44, 1553-1557, (1996)
[14] Laakso, TI; Valimaki, V; Karjalainen, M; Laine, UK, Splitting the unit delay: tools for fractional delay filter design, IEEE Signal Process. Mag., 13, 30-60, (1996)
[15] Lang, M, All-pass filter design and applications, IEEE Trans. Signal Process., 46, 2505-2514, (1998)
[16] Lang, M; Laakso, TI, Simple and robust method for the design of allpass filters using least-squares phase error criterion, IEEE Trans. Circuits Syst. II Analog Digit. Signal Process., 41, 40-48, (1994)
[17] Liand, W; Zhang, YL; Tan, JD; Li, Y, A novel approach to ECG classification based upon two-layered HMMs in body sensor networks, Sensor, 14, 5994-6011, (2014)
[18] W.S. Lu, An argument principle based stability criterion and application to the design of IIR digital filters. in 2006 Proceedings of IEEE International Symposium on Circuits and Systems (2006)
[19] Nguyen, TQ; Laakso, TI; Koilpillai, RD, Eigenfilter approach for the design of allpass filters approximating a given phase response, IEEE Trans. Signal Process., 42, 2257-2263, (1994)
[20] Oja, E, A simplified neuron model as a principal component analyzer, J. Math. Biol., 5, 267-273, (1982) · Zbl 0488.92012
[21] Oja, E, Neural networks, principal components and subspace, Int. J. Neural Syst., 1, 61-68, (1989)
[22] Oja, E, Principal components, minor components, and linear neural networks, Neural Netw., 5, 927-935, (1992)
[23] Quelhas, MF; Petraglia, A, Optimum design of group delay equalizers, Digit. Signal Process., 21, 1-21, (2011)
[24] Regalia, PA; Mitra, SK; Vaidyanathan, PP, The digital all-pass filter: a versatile signal processing building block, Proc. IEEE, 76, 19-37, (1988)
[25] Stancic, G; Nikolic, S, Digital linear phase notch filter design based on IIR all-pass filter application, Digit. Signal Process., 23, 1065-1069, (2013)
[26] L.C. Su, Y.D. Jou, F.K. Chen, Improved computing-efficiency least-squares algorithm with application to all-pass filter design. Math. Probl. Eng. Article ID 249021 (2013). doi:10.1155/2013/249021 · Zbl 1296.94049
[27] Su, LC; Jou, YD; Chen, FK; Sun, CM, Neural network-based IIR all-pass filter design, Circuits Syst. Signal Process., 33, 437-457, (2014)
[28] Tkacenko, A; Vaidyanathan, PP; Nguyen, TQ, On the eigenfilter design method and its applications: a tutorial, IEEE Trans. Circuits and Syst. II Analog Digit. Signal Process., 50, 497-517, (2003)
[29] Tseng, CC, Design of IIR digital all-pass filters using least pth phase error criterion, IEEE Trans. Circuits Syst. II Analog Digit. Signal Process., 50, 653-656, (2003)
[30] Vaidyanathan, PP; Nguyen, TQ, Eigenfilters: a new approach to least-squares FIR design and applications including Nyquist filters, IEEE Trans. Circuits Syst., 34, 11-23, (1987)
[31] Y. Wang, A. Grieco, B. Slutsky, T. Nquyen, Constrained eigenfilter allpass design for photonic systems. in 2012 Proceedings of the 20th European Signal Processing Conference (2012), pp. 2168-2172
[32] Zhang, X; Iwakura, H, Design of IIR digital allpass filters based on eigenvalue problem, IEEE Trans. Signal Process., 47, 554-559, (1999)
[33] Zhang, X; Muguruma, T; Yoshikawa, T, Design of orthonormal symmetric wavelet filters using real all-pass filters, Signal Process., 80, 1551-1559, (2000)
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