In this thesis, an optimization method is used in the design of 1-D IIR digital filters, doubly complementary filter pairs and 2-D IIR digital filters. This method uses genetic algorithm (GA) to minimize the mean square error between the desired and the designed filter responses in order to calculate the coefficients of the filteru27s transfer function. The 1-D IIR filters are designed using cascade structure, and constraints are imposed on the coefficients of the denominator polynomials to ensure stability. In the one-dimensional case, the method is also used to design doubly complementary filter pairs, in which case two filters that are both all-pass complementary and power complementary are designed at the cost of one filter. Based on the same stability criterion, an optimization method is presented for the design of 2-D IIR digital filters with non-separable numerator and separable denominator transfer functions. The advantage of the proposed method is that it produces filters with Canonical Signed-Digit (CSD) coefficients, which not only eliminates the quantization process in digital filter design but also make the designed filter more efficient for high speed DSP applications. Design examples of 1-D IIR filters, doubly complementary filter pairs and 2-D IIR filters are provided in order to demonstrate the usefulness of the presented method.Dept. of Electrical and Computer Engineering. Paper copy at Leddy Library: Theses u26 Major Papers - Basement, West Bldg. / Call Number: Thesis2003 .L555. Source: Masters Abstracts International, Volume: 42-03, page: 1014. Adviser: M. A. Sid-Ahmed. Thesis (M.A.Sc.)--University of Windsor (Canada), 2003.
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机译：本文在设计一维IIR数字滤波器，双互补滤波器对和二维IIR数字滤波器时采用了一种优化方法。该方法使用遗传算法（GA）来最小化所需滤波器响应和设计滤波器响应之间的均方误差，以便计算滤波器传递函数的系数。一维IIR滤波器使用级联结构设计，并且对分母多项式的系数施加了约束以确保稳定性。在一维情况下，该方法还用于设计双互补滤波器对，在这种情况下，要设计两个全通互补和功率互补的滤波器，但要花一个滤波器。基于相同的稳定性准则，提出了一种具有不可分母和分母传递函数的二维IIR数字滤波器设计的优化方法。提出的方法的优点是它可以产生具有标准正负号（CSD）系数的滤波器，这不仅消除了数字滤波器设计中的量化过程，而且使设计的滤波器对于高速DSP应用更加有效。提供一维IIR滤波器，双互补滤波器对和二维IIR滤波器的设计示例，以证明所提出方法的实用性。电气和计算机工程系。莱迪图书馆的纸质副本：论文主要论文-西楼地下室。 /电话号码：Thesis2003 .L555。资料来源：国际硕士摘要，第42卷，第1014页，顾问：M. A. Sid-Ahmed。论文（硕士）-温莎大学（加拿大），2003。
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