A least-square solution to the design problem of 2-D linear-phase FIR filters with arbitrary magnitude responses

In this paper, we present a least-square design algorithm for general 2-D linear-phase FIR filters and obtain a novel closed-form solution for filter coefficients. This solution is derived for the approximation of arbitrarily shaped magnitude responses and is given as an explicit expression in the desired magnitude specifications, making it possible to evaluate very fast the impulse response of the designed filter. It is shown that a further computational reduction can be achieved when this solution is used to design those filters which have centro-symmetric or quadrantally symmetric magnitude responses