Causality-imposed (Kramers-Kronig) relationships between attenuation and dispersion
Causality imposes restrictions on both the time-domain and frequency-domain responses of a system. The Kramers-Kronig (K-K) relations relate the real and imaginary parts of the frequency-domain response. In ultrasonics, K-K relations often are used to link attenuation and dispersion. We review both...
| Veröffentlicht in: | IEEE transactions on ultrasonics, ferroelectrics, and frequency control. - 1999. - 52(2005), 5 vom: 14. Mai, Seite 822-33 |
|---|---|
| 1. Verfasser: | |
| Weitere Verfasser: | , |
| Format: | Aufsatz |
| Sprache: | English |
| Veröffentlicht: |
2005
|
| Zugriff auf das übergeordnete Werk: | IEEE transactions on ultrasonics, ferroelectrics, and frequency control |
| Schlagworte: | Journal Article |
| Zusammenfassung: | Causality imposes restrictions on both the time-domain and frequency-domain responses of a system. The Kramers-Kronig (K-K) relations relate the real and imaginary parts of the frequency-domain response. In ultrasonics, K-K relations often are used to link attenuation and dispersion. We review both integral and differential forms of the frequency-domain K-K relations that are relevant to theoretical models and laboratory measurements. We consider two methods for implementing integral K-K relations for the case of finite-bandwidth data, namely, extrapolation of data and restriction of integration limits. For the latter approach, we discuss the accuracy of K-K predictions for specific classes of system behavior and how the truncation of the integrals affects this accuracy. We demonstrate the accurate prediction of attenuation and dispersion using several forms of the K-K relations relevant to experimental measurements of media with attenuation coefficients obeying a frequency power law and media consisting of resonant scatterers. We also review the time-causal relations that describe the time-domain consequences of causality in the wave equation. These relations can be thought of as time-domain analogs of the (frequency-domain) K-K relations. Causality-imposed relations, such as the K-K and time-causal relations, provide useful tools for the analysis of measurements and models of acoustic systems |
|---|---|
| Beschreibung: | Date Completed 23.08.2005 Date Revised 17.03.2022 published: Print Citation Status PubMed-not-MEDLINE |
| ISSN: | 0885-3010 |