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