Analysis banks, synthesis banks, LPTV filters: Proposition of an equivalence definition application to the design of invertible LPTV filters

Linear Periodical Time Varying (LPTV) ¿lters suffer from a lack of theoretical studies chie¿y regarding construction methods of invertible LPTV ¿lters. Conversely, ¿lter banks have received considerable attention because of large appli- cations in digital communications. In this paper, analysis and synthesis banks of Maximally Decimated Filter Banks (MDFB) are separately related to LPTV ¿lters. Thanks to this de¿nition, perfect reconstruction for a MDFB is math- ematically related to invertibility of LPTV ¿lters. We then make the most of these results to propose a new class of in- vertible LPTV ¿lters relying on a lossless matrix. In a spread spectrum framework, lossless property results in no Bit Er- ror Rate degradation when Spreading is achieved by lossless LPTV ¿lters.