Approximation of digital filters in one and two dimensions

An algorithm for the time domain approximation of discrete systems with a recursion is described. The algorithm iterates towards a solution minimizing the sum of squared differences between the desired and the actual output. Convergence is guaranteed. The scheme is applied to the design of low-pass filters by time domain approximation. The results compare well with other design strategies. We have extended the algorithm to two dimensions. This algorithm is essentially the same iterative scheme used for the one-dimensional case. The two-dimensional iteration achieves better results than the currently used two-dimensional filter synthesis techniques since the starting point of the iteration is the solution of the latter approach. Usually, a few iterations suffice to improve the solution in a satisfactory amount. Convergence is also guaranteed. An example of two-dimensional impulse response approximation is also given as an illustration.