A Weighted Least Square Algorithm for Low-Delay FIR Filters with Piecewise Variable Stopbands
Variable digital filters are useful for various signal processing and communication applications where the frequency characteristics, such as fractional delays and cutoff frequencies, can be varied. In this paper, we propose a design method of variable FIR digital filters with an approximate linear phase characteristic in the passband. The proposed variable FIR filters have some large attenuation in stopband and their large attenuation can be varied by spectrum parameters. In the proposed design method, a quasi-equiripple characteristic can be obtained by using an iterative weighted least square method. The usefulness of the proposed design method is verified through some examples.
[1] C. K. S. Pun, S. C. Chan, K. S. Yeung, and K. L. Ho, "On the design
and implementation of FIR and IIR digital filters with variable frequency
charactericstics," IEEE Trans. Circuits Syst. II, Analog Digit. Signal
Process., vol. 49, no. 11, pp. 689.703, Nov. 2002.
[2] L. R. Rabiner and B. GoldÔÇó ÔÇó"Theory and application of digital signal
processing," Prentice-HallÔÇó ÔÇóNew JerseyÔÇó ÔÇó1975.
[3] T. Shinbo, Y. Sugita, N. Aikawa, T. Kimura, Y. Wakasa, and T. Morichi,
"Design Method of FIR Filters with Variable Piecewise Stopband,"
IEICE Trans. Fundamentals (Japanese Edition), Vol. J87-A, No. 12,
pp.1511-1517, Dec. 2007.
[4] S. Takahashi, N. Aikawa, Y. Wakasa, and M. Nakatani, "FIR Filters with
Variable Stopbands," IEICE Trans. Fundamentals (Japanese Edition),
Vol. J90-A, No. 10, pp.767-770, Oct. 2007.
[5] T. Takahashi, T. Miyata, and N. Aikawa, "An Iterative WLS Chebyshev
Approximation method for the Design of FIR Digital Filters with
Variable Stopbands," IEICE DSP Symposium, B3-1, Nov. 2008.
[6] J. -C. Liu and S. -J. You, "Weighted Least Squares Near-equiripple
Approximation of Variable Fractional Delay FIR Filters," IET Signal
Processing, Vol. 1, no. 2, June 2007.
[7] T. B. Deng, "An improved method for designing variavle recursive
digital filters with guaranteed stability," Signal Processing, vol. 81, pp.
439-446, 2001.
[8] W. R. Lee, L. Caccetta, and V. Rehbock, "Optimal Design of All-Pass
Variable Fractional-Delay Digital Filters," IEEE Transaction on Circuits
and Syatems-I: Regular Papers, Vol. 55, no. 5, June 2008.
[9] L. J. Karam and J. H. McClellan, Complex approximation for FIR filter
design, IEEE Trans. Circuits and Systems, vol. CAS-42, no.3, pp.207-
244, April 1995.
[10] W.-S. Lu, Minimax design of nonlinear-phase FIR filters: A least-pth
approach, Proc. of 2002 IEEE International Symposium on Circuits and
Systems, vol. 1, pp. 409-412, May 2002.
[11] Yong Ching LimÔÇó ÔÇóJu-Hong LeeÔÇó ÔÇóC.K. Chen, and Rong-Huan YangÔÇó ÔÇó"A
Weighted Least Squares Algorithm for Quasi-Equiripple FIR and IIR
Digital Filter Design," IEEE Trans. Signal Processing, Vol.40, No. 3,
pp.551-558, Mar., 1992.
[12] S. -C. Pei and J. -J. Shyu, "Design of Arbitrary Complex Coefficient FIR
Digital Filters by Complex Weighted Least Squares Approximation,"
IEEE Trans. on Circuits and Systems-II: Analog and Digital Signal
Processing, vol. 41, no. 12, pp. 817-820, Dec. 1994.
[13] T. B. Deng, "Weighted least-squares method for designing arbitrarily
1-D FIR digital filters," Signal Processing, vol. 80, pp. 597-613, 2000.
[14] C. Sidney, J. A. Barreto, and I. W. Selesnick, "Iterative Reweighted
Least-Squares Design of FIR Filters," IEEE Trans. on Signal Processing,
vol. 42, no. 11, pp. 2926-2936, Nov. 1994.
[15] A. S. Rukhlenko, "Iterative WLS Design of SAW Bandpass Filters,"
IEEE Trans. on Ultrasonics, Ferroelectrics, and Frequency Control, vol.
54, no. 10, pp. 1930-1935, Oct. 2007.
[1] C. K. S. Pun, S. C. Chan, K. S. Yeung, and K. L. Ho, "On the design
and implementation of FIR and IIR digital filters with variable frequency
charactericstics," IEEE Trans. Circuits Syst. II, Analog Digit. Signal
Process., vol. 49, no. 11, pp. 689.703, Nov. 2002.
[2] L. R. Rabiner and B. GoldÔÇó ÔÇó"Theory and application of digital signal
processing," Prentice-HallÔÇó ÔÇóNew JerseyÔÇó ÔÇó1975.
[3] T. Shinbo, Y. Sugita, N. Aikawa, T. Kimura, Y. Wakasa, and T. Morichi,
"Design Method of FIR Filters with Variable Piecewise Stopband,"
IEICE Trans. Fundamentals (Japanese Edition), Vol. J87-A, No. 12,
pp.1511-1517, Dec. 2007.
[4] S. Takahashi, N. Aikawa, Y. Wakasa, and M. Nakatani, "FIR Filters with
Variable Stopbands," IEICE Trans. Fundamentals (Japanese Edition),
Vol. J90-A, No. 10, pp.767-770, Oct. 2007.
[5] T. Takahashi, T. Miyata, and N. Aikawa, "An Iterative WLS Chebyshev
Approximation method for the Design of FIR Digital Filters with
Variable Stopbands," IEICE DSP Symposium, B3-1, Nov. 2008.
[6] J. -C. Liu and S. -J. You, "Weighted Least Squares Near-equiripple
Approximation of Variable Fractional Delay FIR Filters," IET Signal
Processing, Vol. 1, no. 2, June 2007.
[7] T. B. Deng, "An improved method for designing variavle recursive
digital filters with guaranteed stability," Signal Processing, vol. 81, pp.
439-446, 2001.
[8] W. R. Lee, L. Caccetta, and V. Rehbock, "Optimal Design of All-Pass
Variable Fractional-Delay Digital Filters," IEEE Transaction on Circuits
and Syatems-I: Regular Papers, Vol. 55, no. 5, June 2008.
[9] L. J. Karam and J. H. McClellan, Complex approximation for FIR filter
design, IEEE Trans. Circuits and Systems, vol. CAS-42, no.3, pp.207-
244, April 1995.
[10] W.-S. Lu, Minimax design of nonlinear-phase FIR filters: A least-pth
approach, Proc. of 2002 IEEE International Symposium on Circuits and
Systems, vol. 1, pp. 409-412, May 2002.
[11] Yong Ching LimÔÇó ÔÇóJu-Hong LeeÔÇó ÔÇóC.K. Chen, and Rong-Huan YangÔÇó ÔÇó"A
Weighted Least Squares Algorithm for Quasi-Equiripple FIR and IIR
Digital Filter Design," IEEE Trans. Signal Processing, Vol.40, No. 3,
pp.551-558, Mar., 1992.
[12] S. -C. Pei and J. -J. Shyu, "Design of Arbitrary Complex Coefficient FIR
Digital Filters by Complex Weighted Least Squares Approximation,"
IEEE Trans. on Circuits and Systems-II: Analog and Digital Signal
Processing, vol. 41, no. 12, pp. 817-820, Dec. 1994.
[13] T. B. Deng, "Weighted least-squares method for designing arbitrarily
1-D FIR digital filters," Signal Processing, vol. 80, pp. 597-613, 2000.
[14] C. Sidney, J. A. Barreto, and I. W. Selesnick, "Iterative Reweighted
Least-Squares Design of FIR Filters," IEEE Trans. on Signal Processing,
vol. 42, no. 11, pp. 2926-2936, Nov. 1994.
[15] A. S. Rukhlenko, "Iterative WLS Design of SAW Bandpass Filters,"
IEEE Trans. on Ultrasonics, Ferroelectrics, and Frequency Control, vol.
54, no. 10, pp. 1930-1935, Oct. 2007.
@article{"International Journal of Electrical, Electronic and Communication Sciences:61317", author = "Yasunori Sugita and Toshinori Yoshikawa and Naoyuki Aikawa", title = "A Weighted Least Square Algorithm for Low-Delay FIR Filters with Piecewise Variable Stopbands", abstract = "Variable digital filters are useful for various signal processing and communication applications where the frequency characteristics, such as fractional delays and cutoff frequencies, can be varied. In this paper, we propose a design method of variable FIR digital filters with an approximate linear phase characteristic in the passband. The proposed variable FIR filters have some large attenuation in stopband and their large attenuation can be varied by spectrum parameters. In the proposed design method, a quasi-equiripple characteristic can be obtained by using an iterative weighted least square method. The usefulness of the proposed design method is verified through some examples.
", keywords = "Weighted Least Squares Approximation, Variable FIR Filters, Low-Delay, Quasi-Equiripple", volume = "3", number = "11", pages = "2161-6", }
