Fractional Fourier Transform for Ultrasonic Chirplet Signal Decomposition

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.

[1]  Ingrid Daubechies,et al.  The wavelet transform, time-frequency localization and signal analysis , 1990, IEEE Trans. Inf. Theory.

[2]  Luís B. Almeida,et al.  The fractional Fourier transform and time-frequency representations , 1994, IEEE Trans. Signal Process..

[3]  R. Merletti,et al.  Estimation of shape characteristics of surface muscle signal spectra from time domain data , 1995, IEEE Transactions on Biomedical Engineering.

[4]  Simon Haykin,et al.  The chirplet transform: physical considerations , 1995, IEEE Trans. Signal Process..

[5]  Cagatay Candan,et al.  The discrete fractional Fourier transform , 1999, 1999 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings. ICASSP99 (Cat. No.99CH36258).

[6]  Soo-Chang Pei,et al.  Closed-form discrete fractional and affine Fourier transforms , 2000, IEEE Trans. Signal Process..

[7]  Jafar Saniie,et al.  Model based time-frequency estimation of ultrasonic echoes for NDE applications , 2000, 2000 IEEE Ultrasonics Symposium. Proceedings. An International Symposium (Cat. No.00CH37121).

[8]  J. Saniie,et al.  Model-based estimation of ultrasonic echoes. Part I: Analysis and algorithms , 2001, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[9]  J. Saniie,et al.  Model-based estimation of ultrasonic echoes. Part II: Nondestructive evaluation applications , 2001, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[10]  LJubisa Stankovic,et al.  Time-frequency signal analysis based on the windowed fractional Fourier transform , 2003, Signal Process..

[11]  Imam Samil Yetik,et al.  Beamforming using the fractional Fourier transform , 2003, IEEE Trans. Signal Process..

[12]  J. Saniie,et al.  Ultrasonic flaw detection using discrete wavelet transform for NDE applications , 2004, IEEE Ultrasonics Symposium, 2004.

[13]  N. McDicken,et al.  Filtering of chirped ultrasound echo signals with the fractional Fourier transform , 2004, IEEE Ultrasonics Symposium, 2004.

[14]  J. Saniie,et al.  Ultrasonic data compression via parameter estimation , 2005, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[15]  M. Barbu,et al.  Fractional Fourier transform for sonar signal processing , 2005, Proceedings of OCEANS 2005 MTS/IEEE.

[16]  J. Saniie,et al.  A successive parameter estimation algorithm for chirplet signal decomposition , 2006, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[17]  John J. Soraghan,et al.  The fractional Fourier transform and its application to high resolution SAR imaging , 2007, 2007 IEEE International Geoscience and Remote Sensing Symposium.

[18]  Stéphane Mallat,et al.  A Wavelet Tour of Signal Processing - The Sparse Way, 3rd Edition , 2008 .

[19]  J. Saniie,et al.  Ultrasonic chirplet signal decomposition for defect evaluation and pattern recognition , 2009, 2009 IEEE International Ultrasonics Symposium.

[20]  Ran Tao,et al.  Short-Time Fractional Fourier Transform and Its Applications , 2010, IEEE Transactions on Signal Processing.

[21]  Erdal Oruklu,et al.  Performance evaluation of fractional Fourier transform(FrFT) for time-frequency analysis of ultrasonic signals in NDE applications , 2010, 2010 IEEE International Ultrasonics Symposium.

[22]  Aled T. Catherall,et al.  High resolution spectrograms using a component optimized short-term fractional Fourier transform , 2010, Signal Process..

[23]  YuanChao Zhao,et al.  Blind source separation based on fractional fourier transform , 2011, 2011 International Conference on Mechatronic Science, Electric Engineering and Computer (MEC).

[24]  J. Saniie,et al.  Analysis of fractional fourier transform for ultrasonic NDE Applications , 2011, 2011 IEEE International Ultrasonics Symposium.

[25]  Fabien Millioz,et al.  Circularity of the STFT and Spectral Kurtosis for Time-Frequency Segmentation in Gaussian Environment , 2011, IEEE Transactions on Signal Processing.

[26]  Zheng Bao,et al.  Interference Suppression Algorithm for SAR Based on Time–Frequency Transform , 2011, IEEE Transactions on Geoscience and Remote Sensing.