The methods of spectral analysis based on the use of any model to describe the signal are considered in the article, while using them some assumptions about the behavior of the signal outside the observation interval are made.  The task of spectral analysis or evaluation, in this case, is to find the parameters of the model used, which is selected based on the available a priori information about the studied process.A new spectral analysis method is proposed, which uses the partially classical Prony method, and this method has been improved by replacing the damping sine wave with the use of damped sine wave.Replacing damped sine wave with the use of non-damped sine wave, allows you to very accurately isolate the signal and determine its characteristics against the background of very rich in interference with air space, against the background of radio devices that work legally. For the first time, a fast conversion algorithm was applied to solve the normal equations for finding variables to sequentially determine the parameters of random short-term signals such as amplitude, frequency, and phase.  It is suggested to determine not only static parameters but also the rate of change of these parameters.  Speed of change of parameters allows determining more carefully the signal of the means of silent receiving of information.Modeling of processes of determination of random short-term pulses simulating digital signals of the means of silent receiving of information is carried out, on the basis of the proposed method of spectral analysis, the simulation results are presented in the form of three-dimensional graphs.The main difference is the use not only of the analysis of the amplitude, frequency, phase, and spectrum of the signal but the main analysis of the spectral density of the signal.Analyzes of the simulation result fully confirm the advantages of the proposed method for the determination of random short-term pulses.