Some limits of lattice and lifting structures
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We discuss the relation between lattice and ladder structures for two-channel filter banks. It is well-known that both lattice and ladder steps are powerful enough to generate all perfect reconstructing filter banks provided that the filter coefficients may take arbitrary values in a field. However, we will show that the two concepts differ in general. We relate to two concepts by looking at three properties of the coefficient ring. We discuss a number of incompleteness results of these parameterizations and point out some connections to open problems in group theory.
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