A novel network method designing multirate filter banks and wavelets

A new unified method for designing both para-unitary cosine-modulated FIR filter banks and cosine-modulated wavelets is proposed in this paper. This problem has been formulated as a quadratic-constrained least-squares (QCLS) minimization problem in which all constraint matrices are symmetric and positive-definite. Furthermore, a specific analog neural network whose energy function is chosen as the combined cost of the QCLS minimization problem is built for our design problem in real time. It is quite easy and efficient to obtain analysis and synthesis filters with high stop-band attenuation and cosine-modulated wavelets with compact support by this method. A number of simulations show the effectiveness of this method and the correctness of the theoretical analysis given in this paper.