A dual-chain approach for bottom–up construction of wavelet filters with any integer dilation

Abstract: A dual-chain approach is introduced in this paper to construct dual wavelet filter systems with an arbitrary integer dilation . Starting from a pair of -dual low-pass filters, with , a top–down chain of filters is constructed with consecutive -dual pairs , , and , where and for all , and denotes the number of filter taps of . This enables the formulation of the filter system , with , to be used as the second component of the initial filter system of the bottom–up -dual chain: , constructed bottom–up iteratively, from to , by using both the -duality property of , and the unimodular property of the polyphase Laurent polynomial matrix associated with the filter system . Then the desired dual wavelet filter systems, associated with a and , are given by and . More importantly, the constructive algorithm for this dual-chain approach can be appropriately modified to preserve the symmetry property of the initial -dual pair . For any dilation factor , the dual-chain algorithms developed in this paper provide two systematic methods for the construction of both biorthogonal wavelets and bottom–up wavelets with or without the symmetry property. [Copyright &y& Elsevier]