Wavenumber, group velocity, phase velocity, and frequency-dependent attenuation characterize the propagation of surface waves in dispersive, attenuating media. We use a mathematical model based on the generalized transform to simultaneously estimate these characteristic parameters for later use in joint inversion for near-surface shear wave velocity. We use a scaling factor in the generalized S transform to enable the application of the method in a highly dispersive medium. We introduce a cost function in the -domain to estimate an optimum value for the scaling factor. We also use the cost function to generalize the application of the method for noisy data, especially data with a low signal-to-noise ratio at low frequencies. In that case, the estimated wavenumber is perturbed. As a solution, we estimate wavenumber perturbation by minimizing the cost function, using Simulated Annealing. We use synthetic and real data to show the efficiency of the method for the estimation of the propagation parameters of highly dispersive and noisy media.