A Sequential Constrained Least-Square Approach to Minimax Design of 2-D FIR Filters

The solution to minimax design of 2-D finite-impulse response filter is not necessarily unique. This paper presents a sequential constrained least-square (SCLS) method to obtain a minimax filter with least total squared error. The method converts the minimax design into a series of constrained least-square problems with the same cost function but different magnitude constraints. By producing the sequence of magnitude error bounds with a binary search, the SCLS method has an exponential convergence rate. Design examples of circular, diamond, and fan filters, and comparison with existing methods show that the SCLS method is efficient and absolutely convergent. The resulted filter is not only a minimax filter but also has least total squared error among minimax filters.