Computer-Aided Design Of Two-Dimensional Recursive Digital Filters On The Basis Of Quadrantal Symmetry
A.N. Venetsanopoulos, B. George · International Journal of Modelling and Simulation · 1985
Two-dimensional recursive digital filters have the advantages of flexibility and accuracy, typical of digital processing systems, and the ability to perform the desired filtering with significuntly fewer operations than non-recuvsive filters. In this paper some useful symmetries are exploited in the design of filters with responses which are approximately circularly symmetric. With the imposition of quadrantal symmetry, followed by further symmetry about the 45° line, a particular filter structure is derived using a cascade of causal second order sections. Each section uses only four independent coefficients and possesses a separable denominator, with a resulting simplification of stability testing and stabilization which can now be done by using one dimensional techniques. The Fletcher-Powell non-linear optimization routine is used with a mean squared error criterion, which enables the optimum vulue of the Rain to be incorporated into the objective Function to be minimized.