Hilbert-Twin – A Novel Hilbert Transform-Based Method To Compute The Elastic Modulus In High-Resolution Mechanical Spectroscopy HRMS

Abstract

A novel Hilbert-twin (H-twin) method is introduced as an alternative method for the computation of the resonant frequency for exponentially damped free decays embedded in noise. We also present the comparison among the following methods used to compute the dynamic elastic modulus in solids: the parametric OMI (Optimization in Multiple Intervals), the Yoshida-Magalas (YM) interpolated discrete Fourier transform, the Hilbert-twin (H-twin), and discrete Fourier transform (DFT) methods. It is concluded that the OMI and YM methods are the best methods to compute the elastic modulus from discrete exponentially damped free-elastic decays embedded in unavoidable noise.

Keywords

• elastic modulus
• mechanical spectroscopy
• Hilbert transform
• instantaneous frequency
• interpolated discrete Fourier transform
• Fourier transform