MODELS AND METHODS OF PROCESSING OF INFORMATION ON LOADS OF ACOUSTIC SIGNALS IN TECHNICAL DIAGNOSTIC SYSTEMS

The paper presents one-dimensional discrete-continuous model of power spectrum estimation of the acoustic emission signal, that allows filtering the oscillating components of the acoustic emission signals. The mathematical formalism describing the environment was discussed, initiating the signals of acoustic emission. The problem of spectral analysis and synthesis of acoustic emission signals was solved with the help of Fourier transform. The dependence of acoustic vibrations spectra on the size of the medium parameters and microstructure has been discussed, as well.

Spectral synthesis and residually finite-dimensional algebras

In 2004, a counterexample was given for a 1965 result of R. J. Elliott claiming that discrete spectral synthesis holds on every Abelian group. Since then the investigation of discrete spectral analysis and synthesis has gained traction. Characterizations of the Abelian groups that possess spectral analysis and spectral synthesis, respectively, were published in 2005. A characterization of the varieties on discrete Abelian groups enjoying spectral synthesis is still missing. We present a ring theoretical approach to the issue. In particular, we provide a generalization of the Principal Ideal Theorem on discrete Abelian groups.