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We construct an adaptive asymptotically optimal in order in the weightHilbert space norms signal denoising on the background noise and its energymeasurement, with hight precision near the boundary of the signal. An offeredmethod used the Fourier-Riesz expansion on the orthonormal polynomials, forinstance, Jacobi's polynomials, relative unbounded near the boundary weightfunction. An applications: technical and medical, in particular, cardiacdiagnosis.

Adaptive Optimal Signal (Cardiogram) Processing, with boundary values and energy precisely measurement