Least Total Squared Error Design of 2-D MINIMAX FIR Filters

The minimax design of 2-D (two-dimensional) FIR filters is not necessarily unique since the Haar condition is not generally satisfied. In order to obtain a unique solution, we introduce some additional constraints to the minimax design. This paper presents least total squared error design of 2-D minimax FIR filters which is always unique. This unique minimax solution can be obtained by using a quadratic programming with the primal-dual algorithm. Design examples and comparison with existing methods are provided to demonstrate the effectiveness and efficiency of the proposed method. The resulted filter is not only a minimax filter but also has least total squared error among minimax filters.