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Perfect reconstruction filter banks can be used to generate a variety ofwavelet bases. Using IIR linear phase filters one can obtain symmetryproperties for the wavelet and scaling functions. In this paper we describe allpossible IIR linear phase filters generating symmetric wavelets with anyprescribed number of vanishing moments. In analogy with the well known FIRcase, we construct and study a new family of wavelets obtained by consideringmaximal number of vanishing moments for each fixed order of the IIR filter.Explicit expressions for the coefficients of numerator, denominator, zeroes,and poles are presented.  This new parameterization allows one to design linear phase quadrature mirrorfilters with many other properties of interest such as filters that have anypreassigned set of zeroes in the stopband or that satisfy an almostinterpolating property.  Using Beylkin's approach, it is indicated how to implement these IIR filtersnot as recursive filters but as FIR filters.

Linear Phase Perfect Reconstruction Filters and Wavelets with Even Symmetry