Parameter estimation and signal reconstruction

Abstract In frequency analysis an often appearing problem is the reconstruction of a signal from given samples. Since samples are usually noised, pure interpolating approaches not recommended and appropriate approximation methods more suitable as they can be interpreted kind denoising. Two widely used. One uses reflection coefficients finite sequence Szegő polynomials other one zeros so called Prony polynomial. We show that both closely related. As inverse problem, it’s surprising have in common depend very sensitive on sampling errors. use known properties to estimate positions corresponding Szegő- or Prony-like construct adaptive algorithms calculate these ones. Hereby, we get parameters exponential parts signal, too. Then, (as linear combination such functions) obtained system equations by minimizing residuals with respect norm