Mathematical models and algorithms of computer modeling of spectrometric signals

Abstract

    The technology of computer processing and analysis of data obtained in the process of measuring the energy spectra of X-ray and gamma radiation is gradually replacing the classic analog measurement methods. However, there is a problem of objective evaluation of the effectiveness of different computer analysis methods. Because obtaining reference data is not possible due to the randomness of processes during real experiments. A possible way to solve this problem is computer modeling of an artificial spectrometric signal with known parameters. This will provide an opportunity to determine the probability of detecting detector signals by different methods of mathematical and logical processing.

    The purpose of this work is to develop mathematical models and algorithms for computer modeling of signals with known parameters and investigate the possibility of their use to evaluate the effectiveness of computer methods of recognition and analysis of these signals.

    The article considers two different methods of synthesizing a digital image of a spectrometric signal with the required distribution of pulse amplitudes based on a preloaded template - a tabular function of amplitude distribution.

    The first approach is based on the use of statistical methods and probability ranges for determining pulse amplitudes in the process of digital signal image creation. It allows you to simulate the process of the experiment, gradually forming a signal in which the distribution of amplitudes is always close to the given one. The basis of the second computer modeling approach is the use of deterministic final values of pulse amplitudes distribution in the generated signal. This approach makes it possible to obtain an accurate digital image of the signal with a random distribution of pulses in time, which does not contain statistical deviations from the template. But unlike the first, this method gives the required result only after the end of the entire session of computer modeling of the experiment.

    The article presents some modeling results obtained during numerical experiments based on a computer program developed as a part of the research. When modeling by the first method using an experimentally obtained spectrum or an artificially created idealized template, it is shown that the resulting spectrum contains statistical deviations. But the amplitude distribution function generally corresponds to the tabular function specified in the template.

    The described approaches and modeling algorithms can be used to create digital images of signals with fully defined input data to further test the effectiveness of computer-based methods of spectrometric signal parameters recognition and analysis.