The invariance of current energy fourier spectrum of discrete real signals on finite intervals

Abstract

Digital spectral analysis of signals based on DFT has a number of advantages. However, the transition from analogue to digital methods and techniques is accompanied by a number of undesirable effects. Signals in each subject area usually have their own specifics. Therefore, it is necessary to study these effects in applications of spectral Fourier analysis. Such research is important for three reasons. Firstly, DFT properties are accurate, have their own specificity and significantly differ from the properties of the Fourier transform of continuous signals. Secondly, signals in each subject area have their own specificity. Thirdly, researchers often have prevailing knowledge in some particular domain, rather than in the field of digital signal processing techniques. As a result, in practice, some of the processes and effects arising in applications of digital spectral analysis, unfortunately, escape the attention of researchers which can result in erroneous conclusions. The paper deals with the problems of measuring Fourier spectrum of signals in the base of discrete exponential functions. Methods and algorithms of sliding measurements of energy Fourier spectrum of signals on finite intervals were described. The invariance of current energy Fourier spectrum to moving discrete real signals (which are not periodic) were investigated. The authors identify a new effect of digital spectral analysis — the effect of non-invariance of the current energy Fourier spectrum. Theoretical and practical results of analysis of invariance of current energy Fourier spectrum of tonal components are shown.

The conducted studies allow us:
— to see in a new light the measurement results on finite intervals of current Fourier spectrum and the current energy Fourier spectra of signals;
— give a numerical estimate of the non-invariance of the current energy Fourier spectrum of real tonal components;
— to increase the effectiveness of digital spectral analysis in its many applications, in particular, for solving the problems of detection and identification of hidden periodicities in such subject areas as radar, vibroacoustic diagnostics, passive sonar, biomedicine, etc.