A time domain view of filter banks and wavelets

The authors consider a time domain approach to the reconstruction problem for filter bank and wavelet decompositions. The procedure for the design of general decomposition and reconstruction systems, called generalized lapped transforms (GLTs), is discussed. GLTs include many classical transforms and the discrete-time wavelet transform (DTWT) as special cases. The proposed design procedure is used to design wavelets and DTWT systems. Because of the generality of the framework, regularity and phase conditions can easily be imposed on the wavelet. Also, because the design procedure can be used to design nonuniform band systems, systems with higher frequency resolution than dyadic wavelet-based systems can be designed and realized. A number of design examples are presented