In this paper, we consider the construction of time-varying, support-adapted, oversampled filter banks. In particular, we consider a general class of filter banks, which includes tight frames and orthogonal filter banks as special cases. We show that it is possible to construct a set of boundary filters, which allows the application of the filter bank to one-sided or finite-length signals, without extension of the signal beyond its boundaries. The proposed time varying filter bank retains the properties of the original filter bank, i.e., it implements a frame with the same bounds of the original frame. In the case of orthogonal filter banks, the proposed modified structure implements an orthogonal transform. The construction inherits the ease of implementation and the computational robustness of the lattice filter bank structure.
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