The use of symmetries in the design of multidimensional digital filters. (English) Zbl 0615.93047
Recently the need for processing three-dimensional (3-D) data has arisen in geophysics and computer tomography. In the paper the fundamental symmetries of 3-D digital IIR (infinite impulse response) filters are described and some theorems which give necessary and sufficient conditions that a filter exhibits specifical symmetries are given. The filter is given as the ratio of two polynomials in \(z_ 1\), \(z_ 2\) and \(z_ 3\). Finally, it is shown how the occurrence of these symmetries lead to a reduction of computation time when one uses computer-aided design. Some examples are presented.
Reviewer: D.Stanomir
MSC:
93C55 | Discrete-time control/observation systems |
93B40 | Computational methods in systems theory (MSC2010) |
93E11 | Filtering in stochastic control theory |
62M20 | Inference from stochastic processes and prediction |
93C35 | Multivariable systems, multidimensional control systems |