Grid density for design of one- and two-dimensional FIR filters

The frequency response of a digital filter is often optimised to meet a given set of specifications on a dense grid of frequency points. The density of the frequency grid points must be sufficiently high so that the frequency response of the filter does not violate the specifications at frequencies in between the grid points. However, the computational complexity of the design process and the storage requirements of the computer increase with the number of frequency grid points. In this a detail study of the grid density requirement for the design of FIR filters is presented. The study leads to a useful design rule.