Spectral density correction of a signal at frequency variable transformation

Abstract

The goal of this paper is to determine analytical expression for the spectral density function of a signal, affected by a known frequency transformation, which do not modify the process energy. Such transformations of frequency variable can frequently appear on spectral density function of a signal, due to physical events (e.g. Doppler effect) or mathematical considerations (e.g. changing the coordinate system). In this case, all components of the spectral density function are modified. The formulas are valid for every spectral component and can be used in signal processing, for model simulation or implementation of advanced algorithm. A case study is illustrated on wave spectrum correction.