Investigation of nonlinear transformations of the signal spectrum

We consider various echo-processes having different nature and discuss their mathematical models based on the special nonlinear transformations in the spectral domain. It is shown that the presence of a power polynomial in the spectral domain results in a delay of the external perturbation (signal). The correspondence between the degree of nonlinearity and arising delayed signals is established. The agreement between the numerical results and experimental data is demonstrated for several external signals.