Determination of the group velocity using the time-varying autoregressive TVAR

A time-varying autoregressive ldquoTVARrdquo approach is used for modeling nonstationary signals, and frequency information is then extracted from the TVAR parameters. In this study, we present the application of the TVAR spectrum on the acoustic signal backscattered by an elastic tube. The parameters of this model are determined by the adaptive algorithm. The adaptive methods may be sufficient for the TVAR parameter estimation, if the nonstationay part of a signal changes slowly. The time-varying spectrum ldquoTVARSrdquo (power spectral density) is applied to the analysis of the dispersion of symmetric S0 and antisymmetric A1 circumferential waves propagating around a tube with a radii ratio equal to 0.95. From the TFAR representation obtained, we have estimated the group velocity with precision. These velocities are compared with those computed by the proper mode theory given in the scientific literature. A good agreement is obtained.