Design and implementation of oversampled modulated filter banks
B. Riel · UVic’s Research and Learning Repository (University of Victoria) · 2005
A method for the design and implementation of practical and efficient oversampled filter banks (OFB) is proposed.Specifically, a technique for designing perfect reconstruction (PR) oversampled cosine modulated (CM) and discrete Fourier transform modulated (DFT-M) filter banks (FB) of either odd-or even-stacking type that can be implemented using lifting-based structures is proposed.A generalized, efficient factorization of the polyphase transfer matrices for oversampled modulated filter banks (0-MFB) is proposed that can be applied to the factorization of transfer inatrices resulting from discrete Fourier transform (DFT) or cosine modulation, of either odd-or even-stacking type.This factorization is derived by directly associating the prototype filter coefficients with the modulation matrix coefficients and exploiting redundancies in the modulation transform.By applying the well-known DFT and cosine modulation matrices to this factorization, the general conditions imposed on the resulting factorization matrices are derived for both DFT and cosine modulated filter banks (CMFB) with either odd-or even-stacking type.By exploiting the paraunitary (PU) property of zero-padded square PU matrices, rectangular PU matrices are generated and shown to correspond to PU OFBs.A PU factorization of square matrices is then applied in order to derive a PU factorization of the transfer matrices generated from 0-MFBs.Next, a lifting-based factorization of the rectangular transfer matrices is proposed.This lifting-based factorization extends a lifting-based factorization for square transfer matrices to the case of rectangular transfer matrices.A specific PU lifting-based factorization of square matrices is then applied to the zeropadded square PU matrices related to the rectangular PU transfer matrices corresponding to 0-MFBs.This results in a generalized lifting-based structure for the implementation of PR 0-MFBs.By applying the DFT and cosine modulation matrices, the specific conditions on the lifting-based factorization matrices are derived.These conditions are associated with the design limitations of the FB, such as the length and phase of the analysis and synthesis prototype filters and the relationship between the number of channels M and the subsampling factor N, for each type of modulated filter bank (MFB).Finally, a design method is proposed for the design of 0-MFBs implemented using a lifting-based structure.It is shown that this method provides optimal solutions and results in subband filters having acceptable stopband attenuation.Furthermore, it is shown that FBs with linear phase subband filters can be designed.