Wavelet-based lowpass/bandpass interpolation

Wavelet-based lowpass and bandpass interpolation schemes that are exact for certain classes of signals including polynomials of arbitrarily large degree are discussed. The interpolation technique is studied in the context of wavelet-Galerkin approximation of the shift operator. A recursive dyadic interpolation algorithm makes it an attractive alternative to other schemes. It turns out that the Fourier transform of the lowpass interpolatory function is also (a positive) interpolatory function. The nature of the corresponding interpolating class is not well understood. Extension to the case of multiplicity M orthonormal wavelet bases, where there is an efficient M -adic interpolation scheme, is also given