Computational aspects and applications of a new transform for solving the complex exponentials approximation problem

TL;DR

This paper addresses computational challenges of a new transform for complex exponentials approximation, demonstrating its practical utility through algorithms applied to NMR spectroscopy, time series, and shape reconstruction problems.

Contribution

It introduces computational methods for a recently proposed transform, enabling practical solutions to complex exponentials approximation problems.

Findings

Successful application to NMR spectrometry data

Effective interpolation and extrapolation of time series

Accurate shape reconstruction from moments

Abstract

Many real life problems can be reduced to the solution of a complex exponentials approximation problem which is usually ill posed. Recently a new transform for solving this problem, formulated as a specific moments problem in the plane, has been proposed in a theoretical framework. In this work some computational issues are addressed to make this new tool useful in practice. An algorithm is developed and used to solve a Nuclear Magnetic Resonance spectrometry problem, two time series interpolation and extrapolation problems and a shape from moments problem.