Reconstruction of periodic functions from noisy input data (Q1760944)

The problem of reconstructing a function from noisy Fourier coefficients, which is important for applications, is usually solved by directly summing the Fourier series with normalizing factors that improve the convergence of the series. In this paper, the authors suggest a method for reconstructing a function \(f(x)\) by solving a system (related to the Fourier coefficient of \(f(x)\)) of Fredholm integral equations of the first kind. The authors mention that the method suggested in this paper is intended for recognizing functions with highly noisy Fourier coefficients.