A general time domain approach for the design of perfect reconstruction modulated filter banks

A general temporal approach to the design of modulated filter banks is presented. A general framework has been developed which tackles the general problem of expanding a finite and discrete signal into a lapped, orthogonal or not, time-modulated set of functions. The associated general structure for computing the analysis and synthesis filtering process is presented. The perfect reconstruction conditions are expressed, and it is shown how specific properties can be added to the filters. The design procedure considered allows recursive or nonrecursive solutions to be exhibited (infinite impulse response or finite impulse response). The conditions for restricting the solutions to the class of finite impulse response filters are given. The case of a prototype filter having a support of width 2T is described in order to illustrate the design procedure. The frequency responses of the proposed filters are presented and compared with the response of a classical discrete cosine transform.<>