Performance evaluation of fractional Fourier transform(FrFT) for time-frequency analysis of ultrasonic signals in NDE applications

Recently, there has been a growing attention on fractional Fourier transform (FrFT) for time-frequency analysis. In this investigation, an FrFT-based signal decomposition algorithm is utilized to decompose ultrasonic signals into a linear combination of signal components. As a transformation tool, FrFT is employed to estimate an optimal transform order, which leads to the maximum amplitude response, or the highest kurtosis value in the fractional transform domain. Furthermore, a signal component is obtained by applying a window in the fractional domain and inverse FrFT. In an iterative manner, ultrasonic signals are decomposed into the signal components until a predefined stop criterion is satisfied. Analytical and simulation results show that FrFT is an alternative method to perform high-resolution analysis of nonstationary ultrasonic signals.

I. Introduction

In ultrasonic imaging applications, the detected ultrasonic echoes always interfere with each other due to closed-location, irregular boundaries, different sizes and random orientation of scattering reflectors. The limited resolution of transducer and/or contamination of measurement noise make it more challenging to unravel the desired information using conventional signal processing techniques. Consequently, signal processing methods capable of analyzing the nonstationary and nonlinear behavior of ultrasonic signals for material characterization is highly desirable.