A Study on the Least Squares Reduced Parameter Approximation of FIR Digital Filters
Rounding of coefficients is a common practice in
hardware implementation of digital filters. Where some coefficients
are very close to zero or one, as assumed in this paper, this rounding
action also leads to some computation reduction. Furthermore, if the
discarded coefficient is of high order, a reduced order filter is
obtained, otherwise the order does not change but computation is
reduced. In this paper, the Least Squares approximation to rounded
(or discarded) coefficient FIR filter is investigated. The result also
succinctly extended to general type of FIR filters.
[1] A. Antoniou, Digital Filters: Analysis, Design and Applications. New
York:McGraw-Hill, 1993.
[2] A. Betser and E. Zeheb, "Reduced order IIR approximation to FIR
digital filters," IEEE Trans. Signal Processing, Vol. 39, Nov. 1991,
pp.2540-2544.
[3] B. Beliczynski, I. Kale and G. D. Cain, "Approximation of FIR by IIR
digital filter: an algorithm based on balanced model reduction," IEEE
Trans. Signal Processing, vol. 40, no. 3, Mar. 1992, pp.532-542.
[4] V. Sreeram and P. Agathoklis, "Design of linear-phase IIR filters via
impulse-response gramians," IEEE Trans. Signal Processing, vol. 40,
1992, pp.389-394.
[5] S.C. Peng, B.S. Chen, and B.W. Chiou, "IIR filter design via optimal
hankel-norm approximation," Proc. Inst. Elect. Eng., vol. 139, 1992,
pp.586-590.
[6] K. Glover, "All optimal Hankel-norm approximations of linear
multivariable systems and their ∞-error bounds," Int. Journal of Control,
Vol.39, 1984, pp.1115-1193.
[7] L.Li, L. Xie, , W.Y. Yan, and Y. C. Soh, "Design of Low-Order Linear-
Phase IIR Filters via Orthogonal Projection," IEEE Trans. . Signal
Processing, vol. 47, no. 2, Feb.1999, pp448-457
[8] D. Enns, "Model reduction with balanced realizations: an error bound
and a frequency weighted generalization," in: Proc. 23rd IEEE Conf. on
Decision and Control, Las Vegas, 1984, pp.127-132.
[9] H. E. El-Game1, J. J. Soltis and M. Ahmadi, "Order reduction technique
using the Chebyshev polynomial and its application in digital filter
design," IEE Proc.- Circuits Devices Syst., Vol. 142, No. I, February
1995.
[1] A. Antoniou, Digital Filters: Analysis, Design and Applications. New
York:McGraw-Hill, 1993.
[2] A. Betser and E. Zeheb, "Reduced order IIR approximation to FIR
digital filters," IEEE Trans. Signal Processing, Vol. 39, Nov. 1991,
pp.2540-2544.
[3] B. Beliczynski, I. Kale and G. D. Cain, "Approximation of FIR by IIR
digital filter: an algorithm based on balanced model reduction," IEEE
Trans. Signal Processing, vol. 40, no. 3, Mar. 1992, pp.532-542.
[4] V. Sreeram and P. Agathoklis, "Design of linear-phase IIR filters via
impulse-response gramians," IEEE Trans. Signal Processing, vol. 40,
1992, pp.389-394.
[5] S.C. Peng, B.S. Chen, and B.W. Chiou, "IIR filter design via optimal
hankel-norm approximation," Proc. Inst. Elect. Eng., vol. 139, 1992,
pp.586-590.
[6] K. Glover, "All optimal Hankel-norm approximations of linear
multivariable systems and their ∞-error bounds," Int. Journal of Control,
Vol.39, 1984, pp.1115-1193.
[7] L.Li, L. Xie, , W.Y. Yan, and Y. C. Soh, "Design of Low-Order Linear-
Phase IIR Filters via Orthogonal Projection," IEEE Trans. . Signal
Processing, vol. 47, no. 2, Feb.1999, pp448-457
[8] D. Enns, "Model reduction with balanced realizations: an error bound
and a frequency weighted generalization," in: Proc. 23rd IEEE Conf. on
Decision and Control, Las Vegas, 1984, pp.127-132.
[9] H. E. El-Game1, J. J. Soltis and M. Ahmadi, "Order reduction technique
using the Chebyshev polynomial and its application in digital filter
design," IEE Proc.- Circuits Devices Syst., Vol. 142, No. I, February
1995.
@article{"International Journal of Electrical, Electronic and Communication Sciences:64002", author = "S. Seyedtabaii and E. Seyedtabaii", title = "A Study on the Least Squares Reduced Parameter Approximation of FIR Digital Filters", abstract = "Rounding of coefficients is a common practice in
hardware implementation of digital filters. Where some coefficients
are very close to zero or one, as assumed in this paper, this rounding
action also leads to some computation reduction. Furthermore, if the
discarded coefficient is of high order, a reduced order filter is
obtained, otherwise the order does not change but computation is
reduced. In this paper, the Least Squares approximation to rounded
(or discarded) coefficient FIR filter is investigated. The result also
succinctly extended to general type of FIR filters.", keywords = "Digital filter, filter approximation, least squares,model order reduction.", volume = "2", number = "1", pages = "163-3", }