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 = Σ
m=0
^∞
Σ
n=0
^∞
y
²
(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
= {(z
1
, z
2
): |z
1
| ≤ 1, |z
2
| ≤ 1} the closed unit bidisc, with V
²
= {(z
1
, z
2
): |z
1
| < 1, |z
2
| < 1} the open unit bidisc, and with T
2
= {(z
1
, z
2
): |z
1
| = 1, |z
2
| = 1} the distinguished boundary of the unit bidisc.