Quadrature formulae and asymptotic error expansions for wavelet approximations of smooth functions
SIAM Journal on Numerical Analysis
On the computation of wavelet coefficients
Journal of Approximation Theory
Journal of Computational and Applied Mathematics
From the wavelet series to the discrete wavelet transform-theinitialization
IEEE Transactions on Signal Processing
Initialization of orthogonal discrete wavelet transforms
IEEE Transactions on Signal Processing
The discrete wavelet transform: wedding the a trous and Mallatalgorithms
IEEE Transactions on Signal Processing
B-spline signal processing. II. Efficiency design and applications
IEEE Transactions on Signal Processing
A general sampling theory for nonideal acquisition devices
IEEE Transactions on Signal Processing
Efficient wavelet prefilters with optimal time-shifts
IEEE Transactions on Signal Processing
A sampling theorem for wavelet subspaces
IEEE Transactions on Information Theory - Part 2
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There exist efficient methods to compute the wavelet coefficients of a function f(t) from its point samples f(T[n+@t]), n@?N. However, in many applications the available samples are average samples of the type @!"-"~^~f(T[t+n+@t])u(t)dt, where the averaging function u(t) reflects the characteristic of the acquisition device. In this work, methods to compute the coefficients in a biorthogonal wavelet system from average samples are studied. Error estimations are obtained and using them, the optimal values for the parameters in the proposed approximation rules are calculated. The obtained error estimations can also be applied to the rules that compute the coefficients from point samples, and thus, these estimations can be used to compare and to choose between the different methods proposed in the literature. The methods proposed here also allow us to compute the biorthogonal wavelet coefficients from the coefficients in another biorthogonal wavelet system.