Modulated filter banks and wavelets-a general unified theory

This paper generalizes and unifies well-known results on modulated filter banks (MFBs) and modulated wavelet tight frames (MWTFs). It classifies MFBs based on the discrete cosine or sine transforms that they are associated with. By proper choice of the form of modulation the perfect reconstruction (PR) conditions are seen to be (surprisingly) identical for all classes of MFBs. This has the interesting consequence that optimal MFB prototype designs can be shared across MFB classes. For some classes of MFBs associated MWTFs do not exist, while for others they do. The results cover both orthogonal and biorthogonal MFBs; and the filters could be arbitrary sequences in l²(Z)