Abstract
In Chap. 1 we saw that an ultrasonic system has many components. Those components individually can be complex electromechanical systems such as, for example, the 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 will present a very general modeling framework of linear time-shift invariant (LTI) systems which we will use in order to describe a complete ultrasonic NDE measurement system. Many of the remaining chapters will fill in the details of this general framework and ultimately produce an explicit LTI models of the entire ultrasonic measurement process.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
A. Papoulis, Signal Analysis (McGraw-Hill, New York, 1977)
L.W. Schmerr, S.-J. Song, Ultrasonic Nondestructive Evaluation Systems—Models and Measurements (Springer, New York, 2007)
L.W. Schmerr, Fundamentals of Ultrasonic Phased Arrays (Springer, New York, 2014)
B.A. Auld, General electromechanical reciprocity relations applied to the calculation of elastic wave scattering coefficients. Wave Motion 1, 3–10 (1979)
R.B. Thompson, T.A. Gray, A model relating ultrasonic scattering measurements through liquid-solid interfaces to unbounded medium scattering amplitudes. J. Acoust. Soc. Am. 74, 1279–1290 (1983)
J.D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978)
A. Papoulis, Systems and Transforms with Applications in Optics (McGraw-Hill, New York, 1968)
I.N. Sneddon, The Use of Integral Transforms (McGraw-Hill, New York, 1972)
R. Bracewell, The Fourier Transform and its Applications (McGraw-Hill, New York, 1956)
A. Papoulis, The Fourier Integral and its Applications (McGraw-Hill, New York, 1962)
C.S. Burrus, T.W. Parks, DFT/FFT and Convolution Algorithms (Wiley, New York, 1985)
J.R. Frederick, J.A. Seydel, Improved Discontinuity Detection Using Computer-Aided Ultrasonic Pulse-Echo Techniques (Welding Research Council Bulletin, No. 185, 1973)
D.W. Fitting, L. Adler, Ultrasonic Spectral Analysis for Nondestructive Evaluation (Plenum Press, New York, 1981)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Schmerr, L.W. (2016). Linear Systems and the Fourier Transform. In: Fundamentals of Ultrasonic Nondestructive Evaluation. Springer Series in Measurement Science and Technology. Springer, Cham. https://doi.org/10.1007/978-3-319-30463-2_2
Download citation
DOI: https://doi.org/10.1007/978-3-319-30463-2_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-30461-8
Online ISBN: 978-3-319-30463-2
eBook Packages: Chemistry and Materials ScienceChemistry and Material Science (R0)