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E. Bedrosian, “A Product Theorem for Hilbert Transforms,” Proceedings of IEEE, Vol. 51, No. 5, 1963, pp. 868-869.

has been cited by the following article:

• TITLE: Chirplet Signal and Empirical Mode Decompositions of Ultrasonic Signals for Echo Detection and Estimation

  AUTHORS: Yufeng Lu, Erdal Oruklu, Jafar Saniie

  KEYWORDS: Ultrasound; Hilbert Time-Frequency Representation; Empirical Mode Decomposition; Chirplet Signal Decomposition; Detection; Estimation

  JOURNAL NAME: Journal of Signal and Information Processing, Vol.4 No.2, May 8, 2013

  ABSTRACT: In this study, the performance of chirplet signal decomposition (CSD) and empirical mode decomposition (EMD) coupled with Hilbert spectrum have been evaluated and compared for ultrasonic imaging applications. Numerical and experimental results indicate that both the EMD and CSD are able to decompose sparsely distributed chirplets from noise. In case of signals consisting of multiple interfering chirplets, the CSD algorithm, based on successive search for estimating optimal chirplet parameters, outperforms the EMD algorithm which estimates a series of intrinsic mode functions (IMFs). In particular, we have utilized the EMD as a signal conditioning method for Hilbert time-frequency representation in order to estimate the arrival time and center frequency of chirplets in order to quantify the ultrasonic signals. Experimental results clearly exhibit that the combined EMD and CSD is an effective processing tools to analyze ultrasonic signals for target detection and pattern recognition.