Design of all-pass-based quadrature mirror filter banks using a Lyapunov error criterion

Least-squares design of two-channel quadrature mirror filter banks can be efficiently solved using infinite impulse response all-pass filters without yielding magnitude distortion. This paper exploits a neural network-based Lyapunov energy function to relate the phase objective function of the all-pass-based quadrature mirror filter banks. Applying the neural network architecture and suitable Hopfield-related parameters, the optimal all-pass filter coefficients can be obtained. By further using the parallel combination of the all-pass filters, the two-channel quadrature mirror filter banks can be efficiently designed. Simulation results demonstrate that the proposed approach achieves accurate performance in both reconstruction error and group delay.