Design of two-dimensional FIR digital filters by a two-dimensional WLS technique

For two-dimensional (2-D) FIR filter design, the conventional weighted least squares (WLS) technique rearranges the filter parameters of 2-D form into their corresponding one-dimensional (1-D) form, thus resulting in expensive computation. This paper presents a new computationally efficient WLS technique for the design of 2-D FIR filters. We introduce an updating desired frequency response which implicitly includes the weighting function such that the sum of weighted square errors to be minimized can be represented in a 2-D matrix form. This makes it possible to keep all filter parameters in their natural 2-D form, thereby reducing the computational complexity from O(N^G ) to O(N³). It is confirmed through design examples that the new technique is computationally very efficient and leads to nearly optimal approximations. This technique is suitable for the design of 2-D real zero-phase FIR filters with quadrantal symmetric or antisymmetric frequency response and can also be applied to the design of 1-D FIR filters