O.D. Moskaletz

Harmonic spectrum analysis is one of the most important physical and engineering measurements. Huge role of harmonic analysis in modern science and technology and a high level of spectral instrumentation require a well-developed theory of spectral measurements. One of the main tasks of spectrometry as well as the theory of oscillations and waves is to determine a link between the mathematical concept of physical or instrumental spectrum, that is obtained by measurement. The main task of spectroscopy in the classic concept is to establish the energy distribution frequency function. Spectroscopic data carriers are dynamic signals of electromagnetic nature. The classical model of such signals must be described by finite time functions with finite spectrum. Spectral instrument as a real information system can operate with a finite amount of information; it places restrictions on the number of degrees of freedom of the analyzed signal, which is achieved by the introduction of the truncation operator in spectrum and in time. The connection between mathematics and the instrument spectrum is in the form of linear integral operators relating the complex and the energy spectra, respectively. Kernels of these operators are complex and power spectrum spread functions of spectral device. In other words, the spectral device is characterized by two spectrum spread functions, and its effect is characterized by two linear integral operators. Introduction of complex spectrum spread function is supported by a formalized application of the delta frequency function. This relationship builds on a new concept for optical spectroscopy that is complex instantaneous spectrum. Initial linear integral operator is an operator that links mathematical complex spectrum with a time variable instrumental spectrum. Linear integral operator that links energy mathematical spectrum with instrumental spectrum is a result of time-averaging of square of the modulus of complex instantaneous spectrum. The results are applied to describe diffractive optical spectral device operation. It is noted that a similar description of the spectral instruments takes place in case of sample and instantaneous spectra measuring.