Quantitative Fourier analysis of approximation techniques. I. Interpolators and projectors

@article{Blu1999QuantitativeFA,
  title={Quantitative Fourier analysis of approximation techniques. I. Interpolators and projectors},
  author={Thierry Blu and Michael Unser},
  journal={IEEE Trans. Signal Processing},
  year={1999},
  volume={47},
  pages={2783-2795}
}
We present a general Fourier-based method that provides an accurate prediction of the approximation error as a function of the sampling step T. Our formalism applies to an extended class of convolution-based signal approximation techniques, which includes interpolation, generalized sampling with prefiltering, and the projectors encountered in wavelet theory. We claim that we can predict the L/sup 2/-approximation error by integrating the spectrum of the function to approximate-not necessarily… CONTINUE READING

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