Digital Spectral Analysis by means of the Method of Averag Modified Periodograms Using Binary-Sign Stochastic Quantization of Signals

The method of averaging modified periodograms is one of the main methods for estimating the power spectral density (PSD). The aim of this work was the development of mathematical and algorithmic support, which can increase the computational efficiency of signals digital spectral analysis by this method.The solution to this problem is based on the use of binary-sign stochastic quantization for converting the analyzed signal into a digital code. A special feature of this quantization is the use of a randomizing uniformly distributed auxiliary signal as a stochastic continuous quantization threshold (threshold function). Taking into account the theory of discrete-event modeling the result of binary-sign quantization is interpreted as a chronological sequence of instantaneous events in which its values change. In accordance with this we have a set of time samples that uniquely determine the result of binary-sign quantization in discrete-time form. Discrete-event modeling made it possible to discretize the process of calculating PSD estimates. As a result, the calculation of PSD estimates was reduced to discrete processing of the cosine and sine Fourier transforms for window functions. These Fourier transforms are calculated analytically based on the applied window functions. The obtained mathematical equations for calculating the PSD estimates practically do not require multiplication operations. The main operations of these equations are addition and subtraction. As a consequence, the time spent on digital spectral analysis of signals is reduced.Numerical experiments have shown that the developed mathematical and algorithmic support allows us to calculate the PSD estimates by the method of averaging modified periodograms with a high frequency resolution and accuracy even for a sufficiently low signal-to-noise ratio. This result is especially important for spectral analysis of broadband signals.The developed software module is a problem-oriented component that can be used as part of metrologically significant software for the operational analysis of complex signals.

Prony's method modification of multi frequency signals spectral analysis.

The issues of digital spectral analysis of signals were considered. The possibility of accurate representation of a complex discrete sequence in the form of a linear combination of multiple harmonics without attenuation has been proved and implemented. A finite algorithm modifying the Prony's method was proposed, with a guaranteed arrangement of the poles of the corresponding autoregressive model on the circle of a unit radius. A scheme of economization of the order of the model in conditions of data redundancy in relation to the estimated limited number of harmonic components of the signal was developed.

Measuring the Effectiveness of a Radio-Identification System

Conducted measurements of qualitative informative features for object recognition determined the most effective methods for measuring them. For this purpose, it is proposed to use the method of digital spectral analysis “thermal noise”, which will provide a significant increase in resolution and measurement accuracy of object characteristics. Experimental studies have shown that to increase the likelihood of correct identification of objects by existing radio-technical identification systems, it is necessary to measure the highly informative characteristics of objects - their radar long-range portraits. Measurement of such portraits is proposed to carry out through the use of broadband and especially ultra-wideband signals, with high stability of the complex frequency characteristics of the receiving and transmitting paths of radar stations. In particular, the proposed structure of the construction of an experimental measuring complex and the principle of its operation for measuring radar distance portraits of identification objects.