Design of oversampled DFT-modulated filter banks via modified Newton´s method

This study proposes a modified Newton´s algorithm to design oversampled single-prototype causal FIR nearly perfect reconstruction DFT-modulated filter banks allowing low system delays. The design problem boils down to an unconstrained fourth-order optimisation with respect to the prototype filter (PF), which minimises a weighted sum of the transfer function distortion of the filter bank and the stopband energy of the PF. The analytic forms of the gradient vector and Hessian matrix of the objective function are derived, based on which, a modified Newton´s method with exact line search is proposed to solve the optimisation. The theoretical analysis and numerical experiments are carried out to verify the effectiveness of the algorithm.