Lattice Decomposition of Oversampled Linear-Phase Perfect Reconstruction Filterbanks

In this paper, we show how to compute the parameters of the lattice implementation of linear-phase perfect reconstruction filter banks (OLPPRFBs) (L. Gan and K.-K. Ma, 2003). This lattice implementation is based on a parametrization of the filterbank by a series of left-invertible matrices. It is generic enough to cover orthogonal (para-unitary) and bi-orthogonal filterbanks, as well as any oversampling factor. This lattice has been used mainly for design purposes, where the parameters defining the left-invertible matrices are varied, and the corresponding filterbank response computed, until a desired frequency response is achieved. In this paper, we aim at recovering the parameter matrices from the impulse response of the analysis (and, for high oversampling ratios, synthesis) filters of the filterbank.