Weyl-Heisenberg signal expansions over R in l2(Z) and duality relations involving MDFT filter banks

Modified discrete Fourier transform (MDFT) filter banks are analyzed in relation with Weyl-Heisenberg expansions over R in l₂(Z). This analysis is used to formally derive a result that could sometimes be taken for granted without any proof: the design of perfect reconstruction (PR) MDFT subband coders is equivalent to that of PR MDFT transmultiplexers. The framework of WH expansions over R in l₂(Z) is also used to prove the equivalence between the MDFT transmultiplexer and the biorthogonal frequency division multiplexing/offset quadrature amplitude modulation (BFDM/OQAM) multicarrier system. This analysis also leads to a slightly modified MDFT scheme with a reduced reconstruction delay.