R. R. Nigmatullin, V. A. Toboev

In this paper we suggest a new discrete spectroscopy for analysis of random signals and fluctuations. This discrete spectroscopy is based on successful solution of the modified Prony's problem for the strongly-correlated random sequences. As opposed to the general Prony's problem where the set of frequencies is supposed to be unknown in the new approach suggested the distribution of the unknown frequencies can be found for the strongly-correlated random sequences. Preliminary information about the frequency distribution facilitates the calculations and attaches an additional stability in the presence of a noise. This spectroscopy uses only the informative-significant frequency band that helps to fit the given signal with high accuracy. It means that any random signal measured in t-domain can be "read" in terms of its amplitude-frequency response (AFR) without model assumptions related to the behavior of this signal in the frequency region. The method overcomes some essential drawbacks of the conventional Prony's method and can be determined as the non-orthogonal amplitude frequency analysis of the smoothed sequences (NAFASS). The NAFASS approach can be considered as a prototype of new spectroscopy for short samplings because any random functions can be compared with each other in terms of their AFRs. The possibilities are shown in analysis of the tension of car transmission belts that serves as an actuator of air conditioner compressor.