A new minimax design of two-dimensional FIR filters with reduced group delay

Research effort that has been spent on the minimax design of two-dimensional (2-D) FIR filters mainly focuses on linear-phase filters. Recent methods for the minimax design of 2-D FIR filter with reduced group delay minimize the maximum magnitude of the complex error between the desired and actual frequency responses. The maximum magnitude response and phase response errors are uniquely determined by the maximum magnitude of the complex error, and approximately have the same value. This paper presents a new minimax criterion, where the maximum magnitude of a modified approximation error is minimized, and the maximum absolute phase error is specified. This criterion provides more design flexibilities than that by merely minimizing the maximum complex-error magnitude, and may result in smaller maximum magnitude error and/or phase error. By adding a scaled energy of the complex error to the cost function, we obtain a unique minimax filter with the least complex-error energy among all minimax solutions. The design problem is reformulated in a semi-definite programming (SDP) that allow existing SDP solvers to apply. Design examples demonstrate the effectiveness of the proposed method.