Hilbert transform pitfalls and solutions for ultrasonic NDE applications

Hilbert transform (HT) is a classical tool used to obtain complex analytical signal representation, which is useful for instantaneous frequency and envelop estimation of bandpass signals. However, noise has a significant adverse impact on the performance of HT. Furthermore, the narrowband signal condition in Bedrosian identity makes it problematic to analyze ultrasonic scattering signal using HT. In this investigation, two key issues related to Hilbert transform are addressed for enhanced instantaneous frequency (IF) estimation. First, in order to minimize the effect of the noise, ultrasonic signals are decomposed to multiple narrowbands and instantaneous frequencies within these bands are estimated. Second, a weighted estimated of IF based on envelop estimate of each narrowband is introduced. These methods are applied to various experimental ultrasonic data sets and utilized to examine microstructure scattering, effects of attenuation in large grained materials, and flaw detection in presence of high scattering noise. Simulation studies and experimental results support accuracy of the IF estimation. Enhanced IF estimation techniques provide tractable frequency estimation and makes it possible to quantify spectral shifts due to attenuation, scattering and dispersion effects.