Numerical computation of the cross-covariance sequences of two-dimensional filters and systems

An effective numerical approach is presented for computing the general two-dimensional (2-D) complex integrals arising in the evaluation of cross-covariance sequences of 2-D digital systems. It converts the problem into the solution of a first-order differential equation with its function evaluations being computations of 1-D complex integrals, which can be efficiently accomplished by applying the complex version of the Euclid algorithm. A accurate solution can be obtained if an numerical integration scheme capable of accuracy control is used. To demonstrate the effectiveness of the presented approach, three numerical examples are worked out