On Filter symmetries in a class of tree-structured 2-D nonseparable filter-banks

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On Filter symmetries in a class of tree-structured 2-D nonseparable filter-banks

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Title: On Filter symmetries in a class of tree-structured 2-D nonseparable filter-banks
Author: PATWARDHAN, PG; GADRE, VM
Abstract: In one-dimensional (1-D) filter-banks (FBs), symmetries (or anti-symmetries) in the filter impulse-responses (which implies linear-phase filters) are required for symmetric signal extension schemes for finite-extent signals. In two-dimensional (2-D) separable FBs, essentially, 1-D processing is done independently along each dimension. When 2-D nonseparable FBs are considered, the 2-D filters (2-D signals in general) can have a much larger variety of symmetries (anti-symmetries) than the 1-D case. Some examples of 2-D symmetries possible are quadrantal, diagonal, centro, 4-fold rotational, etc. In this letter, we analyze the filter symmetries in a subclass of tree-structured 2-D nonseparable FBs, whose sampling matrices can be factored as a product of Quincunx sampling matrix and a diagonal matrix. Within this subclass, we distinguish between two types and show that we can have diagonally symmetric filters in Type-I FBs and quadrantally symmetric filters in Type-II FBs. We then discuss how these FBs with quadrantally and diagonally symmetric filters can be used with a symmetric signal extension scheme on finite-extent signals.
URI: http://dx.doi.org/10.1109/LSP.2006.876321
http://hdl.handle.net/10054/201
http://dspace.library.iitb.ac.in/xmlui/handle/10054/201
Date: 2006


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