Determination of quantization error in two-dimensional digital filters

The evaluation of the quantization error in two-dimensional (2-D) digital filters involves the following computation J = Σm=0^∞Σn=0^∞y²(m, n). In this paper general method for the evaluation of J based on Laurent expansion of the integrand is presented. Illustrative example for such a computation is given. Notations: We denote with V^-2= {(z1, z2): |z1| ≤ 1, |z2| ≤ 1} the closed unit bidisc, with V²= {(z1, z2): |z1| < 1, |z2| < 1} the open unit bidisc, and with T2= {(z1, z2): |z1| = 1, |z2| = 1} the distinguished boundary of the unit bidisc.