A time domain view of filter banks and wavelets

K. Nayebi, T.P. Barnwell, M.J.T. Smith
[1991] Conference Record of the Twenty-Fifth Asilomar Conference on Signals, Systems & Computers  
In this paper, we consider a time domain approach to the reconstruction problem for filter bank and wavelet decompositions. The development of this time domain reconstruction theory has resulted in a unified design approach for uniform, nonuniform, low delay, and efficient analysis-synthesis systems. The theory is based on FIR filters and can also be applied to the design of perfect reconstruction systems based on wavelets for multi-resolution analysis-synthesis systems. In this paper, the
more » ... his paper, the procedure for the design of general decomposition and reconstruction systems, called Generalized Lapped Transforms (GLT), is discussed. GLT's include many classical transforms and the discrete-time wavelet transform (DTWT) as special cases. The new 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 included in the paper.
doi:10.1109/acssc.1991.186545 fatcat:zevmqjd32vbb3ih6x7aqgsft3a