Use of Taylor Series Expansions for Time Savings in Computation of Accurate Transducer Pressure Fields

Ernest L. Madsen, Timothy J. Hall, James A. Zagzebski, Michael F. Insana

Research output: Contribution to journalArticlepeer-review


In the method of data reduction used in our laboratory to determine acoustic backscatter coefficients in tissues and tissuelike media, computation of the complex acoustic pressure in an attenuating medium due to a nonfocused disk radiator is required at a large number of field points and over a frequency band of about 1 MHz. Computer CPU time and input/output time can be considerable because of the need to evaluate an integral corresponding to each field point P and frequency, ω. The fact that the frequency dependence of this integral is restricted to a factor in the integrand of the form exp (ikr’ ), where r’ is the dummy variable and k = k( ω ) is the complex wave number, makes the integral part of the expansion in a Taylor series straightfor-ward. The first five terms of the Taylor series have been derived, and tests of the accuracy of the expansion are presented. While maintaining adequate accuracy, the CPU time savings accrued through use of the series corresponds to a factor of 1/7 and an input/output time savings factor of at least 1 /6. (The factor 1 /7 means, e.g., that a CPU time of 35 min without using the Taylor series becomes 5 min using the Taylor series).

Original languageEnglish (US)
Pages (from-to)300-308
Number of pages9
JournalIEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control
Issue number3
StatePublished - May 1987
Externally publishedYes

ASJC Scopus subject areas

  • Instrumentation
  • Acoustics and Ultrasonics
  • Electrical and Electronic Engineering


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