Weighted least squares design of 2-D digital filters

The design of finite impulse response (FIR) filters in one or two-dimensions can be performed with good computational efficiency using weighted least square (WLS) design. This paper presents an improved 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(N⁶) to O(N³). It is confirmed through design examples that our approach is computationally efficient and leads to nearly optimal approximations.