Design of one and two dimensional variable recursive digital filters

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This thesis studies the computer-aided design of a cascade of second-order sections of one-dimensional and wo-dimen- sional variable recursive digital filters. A variable digital filter is a filter whose frequency characteristics can be varied by varying its coefficients. This is achieved by approximating the filter coefficients by functions of the changing spectral parameters of the class of frequency responses in consideration. Thus by varying these parameters the filter characteristics are changed accordingly. Several variable filters design examples are solved to illustrate the method. When compared to invariant filters, a slight reduction in the performance of variable filters were noticed. This is to be expected as the functions are just an approximation of the variation of the filter coefficients. The great flexibility that enable the use of on-line changes considerably overweights this deficiency. In the design of such filters the tp nonlinear iterative optimization technique is proposed. In this optimization technique the Gill-Murray implementation is used. From the examples given it is shown that this method performs better, in its rate of convergence and filter design accuracy than its Quasi-Newton counterparts.