Work

Differential forms of the Kramers-Kronig dispersion relations

Year: 2003

Type: article

Abstract: Differential forms of the Kramers-Krönig dispersion relations provide an alternative to the integral Kramers-Krönig dispersion relations for comparison with finite-bandwidth experimental data. The differential forms of the Kramers-Krönig relations are developed in the context of tempered distributions. Results are illustrated for media with attenuation obeying an arbitrary frequency power law (alpha(omega) = alpha0 + alpha1(absolute value of omega)y). Dispersion predictions using the differential dispersion relations are compared to the measured dispersion for a series of specimens (two polymers, an egg yolk, and two liquids) exhibiting attenuation obeying a frequency power law (1.00 < or = y < or = 1.99), with very good agreement found. For this form of ultrasonic attenuation, the differential Kramers-Krönig dispersion prediction is found to be identical to the (integral) Kramers-Krönig dispersion prediction.

Source: IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control

DOI: 10.1109/tuffc.2003.1176526

Authors: K.R. Waters, M.S. Hughes, J. Mobley, J.G. Miller

Institutions: Washington University in St. Louis, Oak Ridge National Laboratory

Language: English

Topic: Ultrasonics and Acoustic Wave Propagation

Subfield: Mechanics of Materials

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funders: National Institutes of Health, National Heart, Lung, and Blood Institute

Award: Anisotropy in Myocardial Ultrasound