  Perfect reconstruction filter banks can be used to generate a variety of
wavelet bases. Using IIR linear phase filters one can obtain symmetry
properties for the wavelet and scaling functions. In this paper we describe all
possible IIR linear phase filters generating symmetric wavelets with any
prescribed number of vanishing moments. In analogy with the well known FIR
case, we construct and study a new family of wavelets obtained by considering
maximal 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 mirror
filters with many other properties of interest such as filters that have any
preassigned set of zeroes in the stopband or that satisfy an almost
interpolating property.
  Using Beylkin's approach, it is indicated how to implement these IIR filters
not as recursive filters but as FIR filters.
