Design of Stable IIR Digital Filters with Specified Group Delay Errors
The design problem of Infinite Impulse Response (IIR)
digital filters is usually expressed as the minimization problem of
the complex magnitude error that includes both the magnitude and
phase information. However, the group delay of the filter obtained
by solving such design problem may be far from the desired group
delay. In this paper, we propose a design method of stable IIR digital
filters with prespecified maximum group delay errors. In the proposed
method, the approximation problems of the magnitude-phase and
group delay are separately defined, and these two approximation
problems are alternately solved using successive projections. As a
result, the proposed method can design the IIR filters that satisfy the
prespecified allowable errors for not only the complex magnitude but
also the group delay by alternately executing the coefficient update
for the magnitude-phase and the group delay approximation. The
usefulness of the proposed method is verified through some examples.
[1] J. H. McClellan, T. W. Parks and L. R. Rabiner, A Computer program
for designing optimum FIR linear phase digital filters, IEEE Trans. Audio
Electroacoust., vol. AU-21, no.6, pp.506-526, Dec. 1973.
[2] T. W. Parks and J. H. McClellan, Chebyshev approximation for nonrecursive
filters with linear phase, IEEE Trans. Circuit Theory, vol. CT-19,
no.2, pp.189-194, Feb. 1972.
[3] A. A. -Taleb, and Moustafa M. Fahmy, Design of FIR Tow-Dimensional
Digital Filters by Successive Projections, IEEE Trans. Circuits and
Systems, vol. CAS-31, no.9, pp.801-805, Sept. 1984.
[4] R. Ito, T. Fujie, K. Suyama and R. Hirabayashi, Design method of
FIR filters with signed power of two coefficients using a new linear
programming relaxation with triangle inequalities, International Journal
of Innovative Computing, Information and Control, vol. 2, no. 2, pp. 441-
448, April 2006.
[5] M. Akazawa, and M. Ikehara, Simultaneous Approximation of Magnitude
and Group Delay in FIR Digital Filters, IEICE Trans., vol.J87-A, no. 11,
pp. 1395-1402, Nov. 2004.
[6] Z. Lin and Y. Liu, Design of Complex FIR Filters With Reduced Group
Delay Error Using Semidefinite Programming, IEEE Signal Processing
Letters, vol.13, no.9, Sept. 2006.
[7] A. G. Deczky, Synthesis of recursive digital filters using the minimum
p-error criterion, IEEE Trans. Audio Electroacoust., vol. AU-20, pp. 257-
263, Oct. 1972.
[8] W.-S. Lu, S.-C. Pei, and C.-C. Tseng, A weighted least-squares method
for the design of stable 1-D and 2-D IIR digital filters, IEEE Trans. Signal
Processing, vol. 46, pp. 1-10, Jan. 1998.
[9] X. Chen and T.W. Parks, Design of IIR filters in the complex domain,
IEEE Trans. Acoust., Speech and Signal Process., vol. 38, pp. 910-920,
June. 1990.
[10] C.-C. Tseng, Stable IIR diferentiator design using iterative quadratic
programming approach, Signal Process., vol. 80, no. 5, pp. 857-866, 2000.
[11] W.-S. Lu, Design of recursive digital filters with prescribed stability
margin: a parameterization approach, IEEE Trans. Circuits and Syst. II,
vol. 45, pp. 1289-1298, Sept. 1998.
[12] W.-S. Lu, Design of stable minimax IIR digital filters using semidefinite
programming, in Proc. IEEE Int. Symp. Circuits and Syst., vol. 1, Geneva,
Switzerland, pp. 355-358, May 2000.
[13] W.-S. Lu, A unified approach for the design of 2-D digital filters via
semidefinite programming, IEEE Trans. Circuits and Syst. I, Fundam.
Theory Appl., vol. 49, no. 6, pp. 814-826, June 2002.
[14] S.C. Chan and K. M. Tsui, On the design of real and complex FIR filters
with flatness and peak error constraints using semidefinite programmingin
Proc. IEEE int. Symp. Circuits and Syst., vol. III, pp. 125-128, May 2004.
[15] Y. Sugita and N. Aikawa, Design Method of FIR Digital Filters with
Specified Group Delay Errors using Successive Projection, International
Journal of Innovative Computing, Information and Control, vol. 4, no. 2,
pp. 445-455, Feb. 2008.
[16] S. Fukae, N. Aikawa and M. Sato, Complex Chebysev approximation
using successive projections method, IEICE Trans., vol.J80-A, no.7,
pp.1192-1196, July 1997.
[17] S-. C. Pei and I-. I. Yang, Design of a class of time-constrained FIR
digital filters by successive projections, IEEE Trans. Circuits and Systems,
vol. 36, no. 1, pp 164-167, Jan. 1989.
[18] Y. Sugita and N. Aikawa, Design Method of Stable IIR Digital Filters,
The Transactions of the Institute of Electronics, Information and Communication
Engineers A, vol.J85-A, no. 6, pp. 735-740, June 2002.
[19] Y. Sugita and N. Aikawa, A direct design method of minimum phase FIR
Filters, IEICE Trans., Fundamentals, vol.E87-A, no. 10, pp. 1284-1292,
Oct. 2004.
[1] J. H. McClellan, T. W. Parks and L. R. Rabiner, A Computer program
for designing optimum FIR linear phase digital filters, IEEE Trans. Audio
Electroacoust., vol. AU-21, no.6, pp.506-526, Dec. 1973.
[2] T. W. Parks and J. H. McClellan, Chebyshev approximation for nonrecursive
filters with linear phase, IEEE Trans. Circuit Theory, vol. CT-19,
no.2, pp.189-194, Feb. 1972.
[3] A. A. -Taleb, and Moustafa M. Fahmy, Design of FIR Tow-Dimensional
Digital Filters by Successive Projections, IEEE Trans. Circuits and
Systems, vol. CAS-31, no.9, pp.801-805, Sept. 1984.
[4] R. Ito, T. Fujie, K. Suyama and R. Hirabayashi, Design method of
FIR filters with signed power of two coefficients using a new linear
programming relaxation with triangle inequalities, International Journal
of Innovative Computing, Information and Control, vol. 2, no. 2, pp. 441-
448, April 2006.
[5] M. Akazawa, and M. Ikehara, Simultaneous Approximation of Magnitude
and Group Delay in FIR Digital Filters, IEICE Trans., vol.J87-A, no. 11,
pp. 1395-1402, Nov. 2004.
[6] Z. Lin and Y. Liu, Design of Complex FIR Filters With Reduced Group
Delay Error Using Semidefinite Programming, IEEE Signal Processing
Letters, vol.13, no.9, Sept. 2006.
[7] A. G. Deczky, Synthesis of recursive digital filters using the minimum
p-error criterion, IEEE Trans. Audio Electroacoust., vol. AU-20, pp. 257-
263, Oct. 1972.
[8] W.-S. Lu, S.-C. Pei, and C.-C. Tseng, A weighted least-squares method
for the design of stable 1-D and 2-D IIR digital filters, IEEE Trans. Signal
Processing, vol. 46, pp. 1-10, Jan. 1998.
[9] X. Chen and T.W. Parks, Design of IIR filters in the complex domain,
IEEE Trans. Acoust., Speech and Signal Process., vol. 38, pp. 910-920,
June. 1990.
[10] C.-C. Tseng, Stable IIR diferentiator design using iterative quadratic
programming approach, Signal Process., vol. 80, no. 5, pp. 857-866, 2000.
[11] W.-S. Lu, Design of recursive digital filters with prescribed stability
margin: a parameterization approach, IEEE Trans. Circuits and Syst. II,
vol. 45, pp. 1289-1298, Sept. 1998.
[12] W.-S. Lu, Design of stable minimax IIR digital filters using semidefinite
programming, in Proc. IEEE Int. Symp. Circuits and Syst., vol. 1, Geneva,
Switzerland, pp. 355-358, May 2000.
[13] W.-S. Lu, A unified approach for the design of 2-D digital filters via
semidefinite programming, IEEE Trans. Circuits and Syst. I, Fundam.
Theory Appl., vol. 49, no. 6, pp. 814-826, June 2002.
[14] S.C. Chan and K. M. Tsui, On the design of real and complex FIR filters
with flatness and peak error constraints using semidefinite programmingin
Proc. IEEE int. Symp. Circuits and Syst., vol. III, pp. 125-128, May 2004.
[15] Y. Sugita and N. Aikawa, Design Method of FIR Digital Filters with
Specified Group Delay Errors using Successive Projection, International
Journal of Innovative Computing, Information and Control, vol. 4, no. 2,
pp. 445-455, Feb. 2008.
[16] S. Fukae, N. Aikawa and M. Sato, Complex Chebysev approximation
using successive projections method, IEICE Trans., vol.J80-A, no.7,
pp.1192-1196, July 1997.
[17] S-. C. Pei and I-. I. Yang, Design of a class of time-constrained FIR
digital filters by successive projections, IEEE Trans. Circuits and Systems,
vol. 36, no. 1, pp 164-167, Jan. 1989.
[18] Y. Sugita and N. Aikawa, Design Method of Stable IIR Digital Filters,
The Transactions of the Institute of Electronics, Information and Communication
Engineers A, vol.J85-A, no. 6, pp. 735-740, June 2002.
[19] Y. Sugita and N. Aikawa, A direct design method of minimum phase FIR
Filters, IEICE Trans., Fundamentals, vol.E87-A, no. 10, pp. 1284-1292,
Oct. 2004.
@article{"International Journal of Electrical, Electronic and Communication Sciences:56574", author = "Yasunori Sugita and Toshinori Yoshikawa", title = "Design of Stable IIR Digital Filters with Specified Group Delay Errors", abstract = "The design problem of Infinite Impulse Response (IIR)
digital filters is usually expressed as the minimization problem of
the complex magnitude error that includes both the magnitude and
phase information. However, the group delay of the filter obtained
by solving such design problem may be far from the desired group
delay. In this paper, we propose a design method of stable IIR digital
filters with prespecified maximum group delay errors. In the proposed
method, the approximation problems of the magnitude-phase and
group delay are separately defined, and these two approximation
problems are alternately solved using successive projections. As a
result, the proposed method can design the IIR filters that satisfy the
prespecified allowable errors for not only the complex magnitude but
also the group delay by alternately executing the coefficient update
for the magnitude-phase and the group delay approximation. The
usefulness of the proposed method is verified through some examples.", keywords = "Filter design, Group delay approximation, Stable IIRfilters, Successive projection method.", volume = "4", number = "1", pages = "131-6", }
