A closed-form least squares solution to the discrete frequency domain design problem of two-dimensional FIR filters

Abstract

Based on a discrete frequency domain formulation of the design problem of two-dimensional FIR filters, a closed form expression is derived for the matrix of filter coefficients without imposing any assumptions of having a symmetric, antisymmetric or zero-phase frequency response. The matrix in question is derived by minimizing the Frobenius norm of the difference between the matrices of the actual and ideal frequency responses at the points of a frequency grid. The method has the advantages of conceptual and computational simplicity.