An iterative implementation for 2-D digital filters

A 2-D digital filter with a rational frequency response can be expanded into an infinite sequence of filtering operations. Each filtering operation can be implemented by convolution with a low-order 2-D finite-extent impulse response. This sequence of filtering operations can be viewed as an iteration where a new estimate of the output signal is formed from the previous estimate. If a convergence constraint is satisfied, the sequence of estimates will approach the desired output signal. In practice, the number of iterations is finite. Consequently, the frequence response that is actually realized by the iterative implementation is an approximation to the desired rational frequency response.