An l2-stability theorem for multidimensional IIR digital filters

The evaluation of the quantization error in two-dimensional (2-D) digital filters involves the following computation
J = \Sigma\min{m=0}\max{\infin} \Sigma\min{n=0}\max{\infin} y^{2}(m,n)
In this paper a theorem concerning l
2
-stability is given and a general method for the evaluation of J based on a Laurent expansion of the integrand is presented. An illustrative example is given.