A fractional Fourier transform analysis of a bubble excited by an ultrasonic chirp

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Abstract

The fractional Fourier transform is proposed here as a model based, signal processing technique for determining the size of a bubble in a fluid. The bubble is insonified with an ultrasonic chirp and the radiated pressure field is recorded. This experimental bubble response is then compared with a series of theoretical model responses to identify the most accurate match between experiment and theory which allows the correct bubble size to be identified. The fractional Fourier transform is used to produce a more detailed description of each response, and two-dimensional cross correlation is then employed to identify the similarities between the experimental response and each theoretical response. In this paper the experimental bubble response is simulated by adding various levels of noise to the theoretical model output. The method is compared to the standard technique of using time-domain cross correlation. The proposed method is shown to be far more robust at correctly sizing the bubble and can cope with much lower signal to noise ratios. 

Original languageEnglish
Pages (from-to)3264-3270
Number of pages7
JournalJournal of the Acoustical Society of America
Volume130
Issue number5
DOIs
Publication statusPublished - Nov 2011

Keywords

  • coded excitation method
  • generalized-functions
  • size distribution
  • contrast agent

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