TY - JOUR
T1 - Fast and stable least-squares approach for the design of linear phase FIR filters
AU - Okuda, Masahiro
AU - Ikehara, Masaaki
AU - Takahashi, Shin Ichi
N1 - Funding Information:
Manuscript received June 12, 1996; revised December 10, 1997. This work was supported by Japan Society for the Promotion of Science. The associate editor coordinating the review of this paper and approving it for publication was Dr. Sawasd Tantaratana. The authors are with the Department of Electrical Engineering, Keio University, Yokohama, Japan (e-mail: okuda@tkhm.elec.keio.ac.jp). Publisher Item Identifier S 1053-587X(98)03911-7.
PY - 1998
Y1 - 1998
N2 - In this paper, we present a new numerical algorithm for solving the normal equations associated with the least-squares design of linear phase FIR filters. The usual solution methods have a computational complexity of O(N3). Moreover, solving the normal equations with Gaussian elimination commonly yields numerical errors, especially when the filter is long. Here, we convert a least-squares method into the problem of constructing a system of orthonormal functions. The proposed design algorithm needs only O(N2) computations, and numerical errors can be reduced. Some examples are given to show the excellent performance of the algorithm.
AB - In this paper, we present a new numerical algorithm for solving the normal equations associated with the least-squares design of linear phase FIR filters. The usual solution methods have a computational complexity of O(N3). Moreover, solving the normal equations with Gaussian elimination commonly yields numerical errors, especially when the filter is long. Here, we convert a least-squares method into the problem of constructing a system of orthonormal functions. The proposed design algorithm needs only O(N2) computations, and numerical errors can be reduced. Some examples are given to show the excellent performance of the algorithm.
KW - Computational complexity
KW - Least-squares design
KW - Linear-phase fir filters
KW - Orthogonal functions
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U2 - 10.1109/78.678462
DO - 10.1109/78.678462
M3 - Article
AN - SCOPUS:0032097133
VL - 46
SP - 1485
EP - 1493
JO - IEEE Transactions on Acoustics, Speech, and Signal Processing
JF - IEEE Transactions on Acoustics, Speech, and Signal Processing
SN - 1053-587X
IS - 6
ER -