Abstract
We construct an adaptive asymptotically optimal in order in the weight Hilbert space norms signal denoising on the background noise and its energy measurement, with hight precision near the boundary of the signal. An offered method used the Fourier-Riesz expansion on the orthonormal polynomials, for instance, Jacobi's polynomials, relative unbounded near the boundary weight function. An applications: technical and medical, in particular, cardiac diagnosis.
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