New results in multidimensional linear phase filter bank design

We consider the multidimensional version of the problem of linear phase (LP) perfect reconstruction (PR) filter bank design. The filter bank design problem is posed as a matrix completion problem in the context of polynomial matrices having certain symmetries dictated by the linear phase property of the filter bank. We examine the usefulness of a strategy that succeeds in characterization and design of 1D linear phase filter banks via 2D examples. In the 2D quincunx case, for filter banks obtained by McClellan transformations a complete solution can be obtained via this method. The usefuless of the method remains questionable in more general situations. We discuss the issue with examples.