Perfect reconstruction modulated filter banks

New modulated filter banks having the perfect reconstruction property, called perfect reconstruction modulated filter (PRMF) banks, are described. This new framework provides the set of equations to be verified for perfect reconstruction in the general case. In the case of analysis and synthesis filters obtained by the classical cosine modulation of a symmetrical prototype filter h, it gives also the analytic forms of all the possible PRMF banks, with filter length NF shorter than 8.SB, with SB the number of subband channels. Filter banks known as TDAC, MLT, ELT, etc., are particular PRMF banks with NF=2.k.SB, but many other filters exist, with NF odd for example. Odd length filters have a lot of interesting properties.<>