Neural networks design approach for cosine-modulated FIR filter banks and compactly supported wavelets with almost PR property

Abstract

The design problem of paraunitary cosine-modulated FIR filter banks satisfying the perfect-reconstruction (PR) property has been formulated as a quadratic-constrained least-squares (QCLS) minimization problem in which all constraint matrices of the QCLS optimization problem are symmetric and positive definite. In this paper, we propose a neural network to efficiently solve this QCLS optimization problem in real time, whose energy function coincides with the objective function of the above QCLS minimization problem. A detailed analysis of the proposed network shows that the coefficient set of the designed prototype filter is just the output of the network at the minimizer of energy function of the network and, furthermore, that all its minimizers are global minimizers. Additional regularity conditions, which are imposed on the filter bank to obtain the cosine-modulated orthonormal bases of compactly supported wavelets, are transformed into the same formulation as PR condition, i.e. the constraint matrices for regular conditions are also symmetric and positive definite. So a similar method can be used to construct cosine-modulated wavelets. Compared to other design methods, the proposed network has many desirable features such as fast convergence, random initialization, global minimizer to be obtained, high stopband attenuation and so on. Results of computer simulation are presented to support our derivations and analyses.