Upper bound frequencies of two dimensional signals

Two-dimensional (2-D) signals are considered, and expressions calculated for the uniform upper bound frequencies for certain classes of functions such that the contribution of frequencies higher than these bounds is less than some specified value given by the error criterion. Two classes of 2-D signals are considered: signals that can be expressed as a convolution of two functions, each of which is mapped on only one surface (1-D) in a 2-D dimensional space, and signals that can be expressed in the mean as a linear combination of an orthogonal set of functions, where each function in the set is bandlimited and separable