Circuits Syst Signal Process DOI 10.1007/s00034-014-9914-2 Design of Two-Channel Quadrature Mirror Filter Banks Using Minor Component Analysis Algorithm Li-Woei Chen · Yue-Dar Jou · Shu-Sheng Hao Received: 18 September 2013 / Revised: 11 October 2014 / Accepted: 13 October 2014 © Springer Science+Business Media New York 2014 Abstract The design of two-channel quadrature mirror filter banks can be constructed based on real infinite impulse response (IIR) all-pass digital filters without yielding magnitude distortion. The design problem is first formulated as a phase optimization using IIR all-pass filters in the least-squares sense. Then the nonlinear phase opti- mization is further converted into solving an eigenproblem of an appropriate real, symmetric, and positive-definite matrix. In this paper, the minor component analysis algorithm based on the neural learning rule is exploited to the design of eigenfilter. When the learning algorithm achieves convergence, the weights of the neural sys- tem approximate the smallest eigenvector, which are the optimal filter coefficients of the IIR all-pass filters. The simulation results confirm that the proposed neural- based method can achieve accurate performance by incorporating the simple neural model. Keywords All-pass · Eigenfilter · Infinite impulse response · Least-squares · Minor component analysis · Quadrature mirror filter L.-W. Chen · S.-S. Hao School of Defense Science, Chung Cheng Institute of Technology, National Defense University, Tahsi County, Taoyuan 335, Taiwan, ROC e-mail: chen.li.woei@gmail.com S.-S. Hao e-mail: shushenghao@gmail.com Y.-D. Jou (B ) Department of Electrical Engineering, R.O.C. Military Academy, P.O. Box 90602-6, Feng-Shan Dis- trict, Kaohsiung 830, Taiwan, ROC e-mail: ydjou@cc.cma.edu.tw