Minimax Design of 2D FIR Half-Band Filters Using an Efficient Matrix-Based IRLS Algorithm

Abstract

This paper considers the minimax design of two-dimensional (2D) finite impulse response (FIR) half-band filters. First, the design problem is formulated in a matrix form, where the half-band constraints are expressed as a pair of matrix equations. By matrix transformations, the constrained minimax problem is transformed into an unconstrained one. Then, we propose an efficient iterative reweighted least squares (IRLS) algorithm to solve this problem. The weighted least squares (WLS) subproblems arising from the IRLS algorithm are solved using a generalized conjugate gradient (GCG) algorithm. Moreover, the GCG algorithm is guaranteed to converge in a finite number of iterations. In the proposed algorithm, the design coefficients of filters are solved in their matrix form, leading to a great saving in computations and memory space. Design examples and comparisons with existing methods are provided to demonstrate the effectiveness and efficiency of the proposed algorithm.