Weighted least-squares design of linear-phase and arbitrary 2-D complex FIR filters

This paper presents the design of 2-D complex FIR filters using the weighted integral least-squares error criterion (WLS). Both the cases of arbitrary magnitude with linear and arbitrary phase specifications are addressed. The solution of the linear phase case is obtained using the complex Lagrange multiplier formulation to incorporate the necessary constraints for linear phase response. This results in a computationally efficient filter design technique requiring the solution of a Hermitian Toeplitz-block-Toeplitz system of linear equations for which fast algorithms are available. Two illustrative filter design examples are also presented.