Design of NPR DFT-Modulated Filter Banks via Iterative Updating Algorithm

Abstract

In this paper, an efficient algorithm is proposed to design nearly-perfect-reconstruction (NPR) DFT-modulated filter banks. First, the perfect-reconstruction (PR) condition of the oversampled DFT-modulated filter banks in the frequency domain is transformed into a set of quadratic equations with respect to the prototype filter (PF) in the time domain. Second, the design problem is formulated as an unconstrained optimization problem that involves PR condition and stopband energy of the PF. With the gradient vector of the objective function, an efficient iterative algorithm is presented to design the PF, which is updated with linear matrix equations at each iteration. The algorithm is identified as a modified Newton’s method, and its convergence is proved. Numerical examples and comparison with many other existing methods are included to demonstrate the effectiveness of the proposed method.