Design of Alias-free Linear Phase Quadrature Mirror Filter Banks Using Eigenvalue-eigenvector Approach

An eigenvalue-eigenvector approach for the design of two-channel linear phase quadrature mirror filter (QMF) bank is proposed. To reduce the computational complexity, finite-duration impulse response (FIR) low-pass prototype filter of the filter bank is represented by polyphase components. The design problem is formulated to optimize the filter tap weights of the low-pass prototype filter of the QMF bank to minimize an objective function, which is the weighted sum of the square error of the filter bank transfer function at the quadrature frequency, pass-band error and stop-band residual energy of the low-pass prototype filter and measure of reconstruction ripple. The objective function has been minimized by an iterative algorithm. As compared to the existing design techniques, the proposed algorithm gives better performance in terms of mean square error in stop-band, number of iterations required and stop-band edge attenuation. Design examples are presented to validate the effectiveness of the proposed method.