Linear Systems and the Fourier Transform

  • Lester W. SchmerrJr.


In Chap. 1 we saw that an ultrasonic system has many components. Those components individually can be complex electromechanical systems, such as ultrasonic transducers. To model each of the elements that go into an ultrasonic system and how they work together to produce a measured response is a challenging task indeed. In this chapter we present a very general modeling framework of linear time-shift invariant (LTI) systems which we use to describe a complete ultrasonic NDE measurement system. Many of the remaining chapters provide details for this general framework which will be combined to produce an explicit model of the entire ultrasonic measurement process.


Impulse Response Function Ultrasonic System General Modeling Framework Elastic Wave Pulse Time Domain Pulse 
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  1. 2.1.
    A. Papoulis, Signal Analysis (McGraw-Hill, New York, 1977).zbMATHGoogle Scholar
  2. 2.2.
    J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978).Google Scholar
  3. 2.3.
    A. Papoulis, Systems and Transforms with Applications in Optics (McGraw-Hill, New York, 1968).Google Scholar
  4. 2.4.
    I. N. Sneddon, Use of Integral Transforms (McGraw-Hill, New York, 1972).zbMATHGoogle Scholar
  5. 2.5.
    R. Bracewell, Fourier Transform and Its Applications (McGraw-Hill, New York, 1956).Google Scholar
  6. 2.6.
    A. Papoulis, Fourier Integral and Its Applications (McGraw-Hill, New York, 1962).zbMATHGoogle Scholar
  7. 2.7.
    C. S. Burrus and T. W. Parks, DFT/FFT and Convolution Algorithms (Wiley, New York, 1985).Google Scholar
  8. 2.8.
    J. R. Frederick and J. A. Seydel, Welding Research Council Bulletin, No. 185, July 1973.Google Scholar
  9. 2.9.
    D. W. Fitting and L. Adler, Ultrasonic Spectral Analysis for Nondestructive Evaluation (Plenum, New York, 1981).Google Scholar

Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • Lester W. SchmerrJr.
    • 1
  1. 1.Iowa State UniversityAmesUSA

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