TY - JOUR
T1 - Least-squares approach to IIR digital filters and an application to equiripple solutions
AU - Okuda, Masahiro
AU - Ikehara, Masaaki
AU - Takahashi, Shin Ichi
PY - 1998/7
Y1 - 1998/7
N2 - This paper formulates the modified least-squares method presented by Mullis in a general form so that weighting can be applied. Then, an algorithm is proposed with which a least-squares approximation can be derived for an IIR digital filter, by solving iteratively a system of equations. The method is extended to a complex Chebyshev approximation that minimizes the maximum magnitude of the complex error, by multiplying the weight, which is newly derived in this paper, with the modified least-squares error. The method is compared with a conventional complex Chebyshev approximation by means of a computer simulation and the effectiveness of the proposed method is demonstrated.
AB - This paper formulates the modified least-squares method presented by Mullis in a general form so that weighting can be applied. Then, an algorithm is proposed with which a least-squares approximation can be derived for an IIR digital filter, by solving iteratively a system of equations. The method is extended to a complex Chebyshev approximation that minimizes the maximum magnitude of the complex error, by multiplying the weight, which is newly derived in this paper, with the modified least-squares error. The method is compared with a conventional complex Chebyshev approximation by means of a computer simulation and the effectiveness of the proposed method is demonstrated.
KW - Equiripple approximation
KW - Gram-Schmidt orthogonalization
KW - IIR digital filter
KW - Weighted modified least-squares method
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U2 - 10.1002/(SICI)1520-6440(199807)81:7<28::AID-ECJC4>3.0.CO;2-X
DO - 10.1002/(SICI)1520-6440(199807)81:7<28::AID-ECJC4>3.0.CO;2-X
M3 - Article
AN - SCOPUS:0032121997
SN - 1042-0967
VL - 81
SP - 28
EP - 36
JO - Electronics and Communications in Japan, Part III: Fundamental Electronic Science (English translation of Denshi Tsushin Gakkai Ronbunshi)
JF - Electronics and Communications in Japan, Part III: Fundamental Electronic Science (English translation of Denshi Tsushin Gakkai Ronbunshi)
IS - 7
ER -