Wavelets generated by IIR filter banks
The relation between orthogonal finite impulse response filter banks and orthonormal bases of compactly supported wavelets has been established by Daubechies (1988). Building on this result, the authors use infinite impulse response (IIR) filter banks to construct more general orthonormal wavelet bases, which have infinite support, but rapid decay. They give a complete constructive method which gives all rational orthogonal two-channel filters banks. A family of wavelets is developed which have similar smoothness and moment properties to those of Daubechies. Wavelet bases are derived for the space of piecewise polynomial functions, which are alternatives to the Battle-Lemarie bases (Battle, 1987; Lemarie, 1988) and have the desirable property of being realizable. Relevant design exchanges are presented.<<ETX>>