Approximation from shift-invariant spaces by integral operators
SIAM Journal on Mathematical Analysis
Quantitative Fourier analysis of approximation techniques. I.Interpolators and projectors
IEEE Transactions on Signal Processing
Generalized sampling theorems in multiresolution subspaces
IEEE Transactions on Signal Processing
On the approximation power of convolution-based least squaresversus interpolation
IEEE Transactions on Signal Processing
Multivariate MIMO FIR inverses
IEEE Transactions on Image Processing
Quasi-Interpolating Spline Models for Hexagonally-Sampled Data
IEEE Transactions on Image Processing
Quasi-interpolation by means of filter-banks
IEEE Transactions on Signal Processing
| Hi-index | 35.69 |
It is well known that, under appropriate hypotheses, a sampling formula allows us to recover any function in a principal shift-invariant space from its samples taken with sampling period one. Whenever the generator of the shift-invariant space satisfies the Strang-Fix conditions of order r, this formula also provides an approximation scheme of order r valid for smooth functions. In this paper we obtain sampling formulas sharing the same features by using a rational sampling period less than one. With the use of this oversampling technique, there is not one but an infinite number of sampling formulas. Whenever the generator has compact support, among these formulas it is possible to find one whose associated reconstruction functions have also compact support.