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A Quantitative Fourier Analysis of the Linear Approximation Error by Wavelets

T. Blu, M. Unser

Wavelet Applications Workshop, Monte Verità TI, Swiss Confederation, September 28-October 2, 1998.



We introduce a simple method—integration of the power spectrum against a Fourier kernel—for computing the approximation error by wavelets. This method is powerful enough to recover all classical L2 results in approximation theory (Strang-Fix theory), and also to provide new error estimates that are sharper and asymptotically exact.


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