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

TL;DR

This paper introduces an adaptive method for denoising and precisely measuring the energy of signals, especially near boundaries, using Fourier-Riesz expansion with orthogonal polynomials like Jacobi's, applicable in medical diagnostics such as cardiology.

Contribution

It presents a novel adaptive approach that achieves asymptotic optimality in signal denoising and energy measurement near boundaries using orthogonal polynomial expansions.

Findings

High-precision boundary energy measurement achieved

Method demonstrates effectiveness in medical signal processing

Adaptive denoising outperforms traditional techniques

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.