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Advances in Acoustics and Vibration
Volume 2012 (2012), Article ID 480473, 13 pages
Research Article

Fractional Fourier Transform for Ultrasonic Chirplet Signal Decomposition

1Department of Electrical and Computer Engineering, Bradley University, Peoria, IL 61625, USA
2Department of Electrical and Computer Engineering, Illinois Institute of Technology, Chicago, IL 60616, USA

Received 7 April 2012; Accepted 31 May 2012

Academic Editor: Mario Kupnik

Copyright © 2012 Yufeng Lu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A fractional fourier transform (FrFT) based chirplet signal decomposition (FrFT-CSD) algorithm is proposed to analyze ultrasonic signals for NDE applications. Particularly, this method is utilized to isolate dominant chirplet echoes for successive steps in signal decomposition and parameter estimation. FrFT rotates the signal with an optimal transform order. The search of optimal transform order is conducted by determining the highest kurtosis value of the signal in the transformed domain. A simulation study reveals the relationship among the kurtosis, the transform order of FrFT, and the chirp rate parameter in the simulated ultrasonic echoes. Benchmark and ultrasonic experimental data are used to evaluate the FrFT-CSD algorithm. Signal processing results show that FrFT-CSD not only reconstructs signal successfully, but also characterizes echoes and estimates echo parameters accurately. This study has a broad range of applications of importance in signal detection, estimation, and pattern recognition.