A realizable paraunitary perfect reconstruction QMF bank based on IIR filters

In this paper, we address the problem of realizing a paraunitary perfect reconstruction quadrature mirror filter bank based on IIR filters. The bank is devoted to the analysis of transient phenomena, in particular of seismic traces from which the information of the arrival times of the incoming phases must be extracted. We have shown recently (Lo Presti and Olmo, To be submitted) that this task requires the realization of highly selective filter banks, which makes it necessary to resort to IIR solutions. The details of the implementation of such a filter bank are addressed, with particular emphasis on the border effects which arise due to the presence of noncausal filters. Solutions which avoid both the signal scattering and the initial condition errors are proposed for the particular class of signals at hand, namely vanishing ones. The addition of zeros at the head and tail of the sequence can effectively combat distorsion in the recovered signal, and at the same time does not affect the coefficients of the decomposition. A signal support enlargement can be tolerated for the application at hand, which is focused on the data analysis. Rules are given in order to evaluate the number of zeros to be added, as a function of the employed filters. The results in terms of the reconstruction error are rather satisfactory for the considered class of signals.