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Mathematical Problems in Engineering
Volume 2013, Article ID 249021, 8 pages
Research Article

Improved Computing-Efficiency Least-Squares Algorithm with Application to All-Pass Filter Design

1Department of Computer and Information Science, R.O.C. Military Academy, Fengshan District, Kaohsiung 830, Taiwan
2Department of Electrical Engineering, R.O.C. Military Academy, P.O. Box 90602-6, Fengshan District, Kaohsiung 830, Taiwan
3Department of Computer Science and Information Engineering, Southern Taiwan University of Science and Technology, Yongkang District, Tainan 710, Taiwan

Received 2 April 2013; Accepted 26 May 2013

Academic Editor: Ker-Wei Yu

Copyright © 2013 Lo-Chyuan Su et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


All-pass filter design can be generally achieved by solving a system of linear equations. The associated matrices involved in the set of linear equations can be further formulated as a Toeplitz-plus-Hankel form such that a matrix inversion is avoided. Consequently, the optimal filter coefficients can be solved by using computationally efficient Levinson algorithms or Cholesky decomposition technique. In this paper, based on trigonometric identities and sampling the frequency band of interest uniformly, the authors proposed closed-form expressions to compute the elements of the Toeplitz-plus-Hankel matrix required in the least-squares design of IIR all-pass filters. Simulation results confirm that the proposed method achieves good performance as well as effectiveness.