On a time-domain representation of the Kramers-Kronig dispersion relations

The development of Kramers-Kronig dispersion relations is typically carried out in the frequency domain. An alternative approach known as the time-cau sal theory develops dispersion relations for media with attenuation obeying a frequency power law through analysis in the time domain [T. L, Szabo, J. Acoust. Sec. Am. 96, 491-500 (1994)]. Although both approaches predict ide ntical dispersion relations, it is perceived that these two approaches are distinct from each other. It is shown, however, that the time-causal theory is in essence a time-domain formulation of the Kramers-Kronig dispersion r elations for the special case of media with attenuation obeying a frequency power law. Additionally, it is shown that time-domain representations of t he Kramers-Kronig dispersion relations are available for a broader class of media than Simply those with power law attenuation. The time-causal theory and the Kramers-Kronig dispersion relations can be viewed as two complemen tary, yet equivalent, approaches to the study of dispersion. (C) 2000 Acous tical Society of America.