Oversampled Wilson-type cosine modulated filter banks with linear phase

We introduce Wilson filter banks (WFBs) as a new type of cosine modulated filter banks (CMFBs) corresponding to the discrete-time Wilson expansion. WFBs allow linear phase filters in all channels. We formulate perfect reconstruction (PR) conditions for oversampled and critically sampled WFBs and show that PR WFBs correspond to PR DFT filter banks with twice the oversampling factor. Generalizing WFBs, we then propose the new family of "even-stacked" CMFBs allowing both PR and linear phase filters in all channels. This CMFB family contains WFBs as well as CMFBs introduced by Lin and Vaidyanathan (1995). Finally, after extending conventional ("odd-stacked") CMFBs to the oversampled case, we formulate unified PR conditions for both even- and odd-stacked oversampled and critically sampled CMFBs. We show that PR CMFBs are always related to PR DFT filter banks of the same stacking type and with twice the oversampling factor.