# Variable Bandwidth Adaptive Notch Filter

## Main Article Content

## Abstract

This paper presents the algorithm for adjusting bandwidth of second-order adaptive IIR notch filter with constrained poles and zeros that works with the plain gradient algorithm to adjust its coefficient. The proposed method can increase the speed of convergence of the filter, especially, when the optimum solution is far away from the initial value of adjustment.

## Article Details

Copyright @2021 Engineering Transactions

Faculty of Engineering and Technology

Mahanakorn University of Technology

## References

M. Ferdjallah and R. E. Barr, “Adaptive digital notch filter desing on the unit circle for removal of powerline noise from biomedical signals,” IEEE Trans. Biomed. Eng., vol. 41, no. 6, pp. 529-536, Jun. 1994.

A. K. Ziarani and A. Konrad, “A nonlinear adaptive method of elimination of power line interference in ECG signals,” IEEE Trans. Biomed. Eng., vol. 49, no. 6, pp. 540-547, Jun. 2002.

P. S. Hamilton, “A comparison of adaptive and nonadaptive filters for reduction of powerline interference in the ECG,” IEEE Trans. Biomed. Eng., vol. 43, no. 1, pp. 105-109, Jan. 1996.

N. V. Thakor and Y. S. Zhu, “Application of adaptive filtering to ECG analysis: Noise cancellation and arrhythmia detection,” IEEE Trans. Biomed. Eng., vol. 38, no. 8, pp. 785-794, Aug. 1991.

W. K. Ma, Y. T. Zhang, and F. S. Yang, “A fast recursive-least-squares adaptive notch filter and its applications to biomedical signals,” Med. Biol. Eng. Comput., vol.37, no. 1, pp. 99-103, Jan. 1999.

S.-C Pei and C.-C. Tseng, “Elimination of AC interference in electrocardiogram using IIR notch filter with transient suppression,” IEEE Trans, Biomed. Eng., vol. 42, no. 11, pp. 1128-1132, Nov. 1995.

J. W. Choi and N. I. Cho, “Suppression of narrow-band interference in DS-spread spectrum systems using adaptive IIR notch filter,” Signal processing, vol. 82, no. 12, pp. 2003-2013, Dec. 2002.

I. Claesson and A. Rossholm, “Notch filtering of humming GSM mobile telephone noise,” in Proc. Int. Conf. Inf., Commun. Signal Process., 2005, pp. 1320-1323.

M. Mojiri, M. Karimi-Ghartemani, and A. Bakhshai, “Estimation of power system frequency using an adaptive notch filter,” IEEE Trans. Instrum. Meas., vol. 56, no. 6, pp. 2470-2477, Dec. 2007.

W. Loetwassana, R. Punchalard, and W. Silaphan, “Adaptive howling canceller using adaptive IIR notch filter: simulation and implementation,” in Proc. 2003 IEEE Int. Neural Networks and Signal Process. (ICNNSP’ 03), Nanjing, China, Dec. 2003, pp. 848-851.

W. Loetwassana, R. Punchalard, A. Lorsawatsiri, J. Koseeyaporn, and P. Wardkeing, “Adaptive howling suppressor in an audio amplifier system,” in Proc. 2007 Asia-Pacific Conf. Commun. (APCC’07), Bangkok, Thailand, Oct. 2007, pp. 445-448.

S. M. Kuo and J. Chen, “New adaptive IIR notch filter and its application to howling control in speakerphone system,” IEE Electronics Lett., vol. 28, no. 8, pp. 764-766, Apr. 1992.

J. Wei, L. Du, Z. Chen, and F. Yin, “A new algorithm for howling detection,” in Proc. 2003 IEEE Int. Symp. Circuits Syst. (ISCAS’03), vol. 4, Bangkok, Thailand, May 2003, pp. 409-411.

M. Vlcek and P. Zahradnik, “Fast analytical design algorithms for FIR notch filters,” IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 51, no. 3, pp. 608-623, Mar. 2004.

S. C. Dutta Roy, B. Kumar, and S. B. Jain, “FIR notch filter design-A review,” Facta Universitatis, vol. 14, no. 3, pp. 295-327, Dec. 2001.

Y. V. Joshi and S. C. Dutta Roy, “Design of IIR digital notch filters,” Circuits, Syst., Signal Process., vol. 16, no. 4, pp. 4185-427, Jul. 1997.

M. Makundi, T. I. Laakso, and L. Yaohui, “Asynchronous implementation of transient suppression in tunable IIR filters,” in Proc. Int. Conf. Digital Signal Process., 2002, vol. 2, pp. 815-818.

Y. Prudat, J.-M. Vesin, “Multi-signal extension of adaptive frequency tracking algorithms.” Signal Processing, vol. 89, pp. 963-973, 2009.

R. Punchalard, J. Keseeyaporn, P. Wardkein, “Indirect frequency estimation based on second-order adaptive FIR notch filter,” Signal Processing, vol. 89, no. 7, pp. 1428-1435, Jul. 2009.

R. Punchalard et al., “Direct frequency estimation based adaptive algorithm for a second-order adaptive FIR notch filter,” Signal Processing, vol. 88, no. 2, pp. 315-325, Feb. 2008.

R. Punchalard et al., “Adaptive IIR notch filter based on new error criteria,” Signal Processing, vol. 88, no. 3, pp. 685-703, Mar. 2008.

R. Punchalard, J. Koseeyaporn, P. Wardkein, “Adaptive IIR notch filter using a modified sign algorithm,” Signal Processing, vol. 89, no. 2, pp. 239-243, Feb. 2009.

W. Loetwassana, R. Punchalard, J. Koseeyaporn, P. Wardkein, “Unbiased plain gradient algorithm for a second-order adaptive IIR notch filter with constrained poles and zeros,” Signal Processing, vol. 90, no. 8, pp.2513-2520, Aug. 2010.

R. Punchalard et al., “Unbiased equation error adaptive IIR notch filter,” in Proc. 2007 IEEE Region 10 Conf.. (TENCON’07), 2007, pp. 1-3.

R. Punchalard et al., “Direct frequency estimation based Kalman adaptive IIR notch filter : State-Space Approach,” in Proc. 2006 IEEE Region 10 Conf.. (TENCON’06), 2007, pp. 1-4.

R. Punchalard et al., “Convergence speed improvement for a variable step-size plain gradient algorithm by using variable notch bandwidth technique,” in Proc. 2003 Int. Symp. On Image and signal process. and analysis (ISPA’03), 2003, pp. 788-792.

R. Punchalard et al., “Unbiased plain gradient algorithm for adaptive IIR notch filter with constrained poles and zeros,” in Proc. 2007 IEEE Region 10 Conf.. (TENCON’07), 2007, pp. 1-4.

R. Punchalard et al., “Inverse tangent based algorithm for constrained adaptive IIR notch filter,” in Proc. 2006 IEEE Region 10 Conf.. (TENCON’06), 2006, pp. 1-4.

R. Punchalard et al., “Mean square error analysis of the PG algorithm for adaptive IIR notch filter with constrained poles and zeros using power spectral density method,” in Proc. 2008 IEEE Asia pacific Conf. on circuit. sys. (APCCAS’08), 2008, pp. 193-196.

R. Punchalard, “On adaptive IIR lattice notch filter using a robust variable step-size for the detection of sinusoid,” in Proc. 2002 IEEE int. Conf. Com. Sys. (ICCS’02), 2002, vol. 2, pp. 800-804.

R. Punchalard et al., “Statistical analysis of an unbiased plain gradient algorithm for a constrained adaptive IIR notch filter,” in Proc. 2008 Asia Pacific Conf. Comm. (APCC’08), 2008, pp. 1-5.

R. Punchalard et al., “Unbiased constrained adaptive IIR notch filter using direct frequency estimation algorithm,” in Proc. 2007 Asia Pacific Conf. Comm. (APCC’07), 2007, pp. 453-456.

R. Punchalard et al., “Inverse tangent based adaptive IIR notch filter,” in Proc. 2006 IEEE Asia pacific Conf. on circuit. sys. (APCCAS’06), 2006, pp. 1208-1211.

R. Punchalard et al., “The reduction of gradient noise in gradient-based algorithm by using variable step-size technique,” in Proc. 2000 IEEE Asia pacific Conf. on circuit. sys. (APCCAS’00), 2000, pp. 415-418.

R. Punchalard et al., “Modified adaptive IIR notch filter based on direct frequency estimation algorithm,” in Proc. 2006 IEEE int. Conf. Com. Sys. (ICCS’06), 2006, pp. 1-4.

J. F. Chicharo and T. S. Ng, “Gradient-based adaptive IIR notch filtering for frequency estimation,” IEEE Trans. Acoust., Speech, Signal Processing, vol. 38, pp. 769-777, May 1990.

Y. Xiao, Y. Takeshita, and K. Shida, “Steady-state analysis of a plain gradient algorithm for a second-order adaptive IIR notch filter with constrained poles and zeros,” IEEE Trans. Circuits Syst. II., vol. 48, pp. 733-740, July 2001.

Y. Xiao, Y. Takeshita, and K. Shida, “Tracking properties of a gradient based second-order adaptive IIR notch filter with constrained poles and zeros,” IEEE Trans. Signal Processing, vol. 50, pp. 878-888, Apr. 2002.

N. I. Cho, C. H. Choi, and S. U. Lee, “Adaptive line enhancement by using and IIR lattice notch filter,” IEEE Trans. Acoust., Speech, Signal Process., vol. 37, no. 4, pp. 585-589, Apr. 1989.

K. Martin and M. T. Sun, “Adaptive filters suitable for real-time spectral analysis,” IEEE Trans. Circuits Syst., vol. CAS-33, no. 2, pp. 218-229, Feb. 1996.

A. Nehorai, “A minimal parameter adaptive notch filter with constrained poles and zeros,” IEEE Trans. Acoust., Speeech, Signal Process., vol. ASSP-33, no. 4, pp.983-996, Jul. 1985.

S.-C. Pei and C.-C. Tseng, “Adaptive IIR notch filter based on least mean p-power error criterion,” IEEE Trans. Circuit, Syst., vol. 40, no. 8, pp. 525-529, Aug. 1993.

Y. Xiao, Y. Tadokoro, and Y. Kobayashi, “A new memoryless nonlinear gradient algorithm for a second-order adaptive IIR notch filter and its performance analysis,” IEEE Trans. Circuits Syst. II, Analog Digit. Signal Process., vol. 45, no. 4, pp. 462-472, Apr. 1998.

A. V. Oppenheim and W. R. Schafer, Digital signal processing, Englewood Cliffs, NJ: Prentice Hall, 1989.

Simon Haykin, Adaptive filter theory, Fourth edition, Prentice Hall, 2002.

J. Zhou and G. Li, “Plain gradient based direct frequency estimation using second-order constrained adaptive IIR notch filter,” Electron. Lett., vol. 40, no. 5, 2002.

G. G. Proakis, and D. G. Manolakis, Digital signal processing: principles, algorithms, and applications, Macmillan Publishing Company, 1992.

A. Mvuma, S. Nishimura, and T. Hinamoto, “Adaptive optimization of notch bandwidth of an IIR filter used to suppress narrow-band interference,” in Proc. 2002 IEEE Int. Symp. On circuit. sys. (ISCAS’02), 2002, vol. 5, pp. v-341-v-344.