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| Content Provider | Springer Nature Link |
|---|---|
| Author | Astaf’ev, M. G. Grafov, B. M. |
| Copyright Year | 2010 |
| Abstract | The work analyzes the existing ambiguity in the ways of application of theoretical relationships derived for infinite numeric series to real experiments of finite duration. A new calculation technique based on constructing a two-dimensional discrete time grid is used as a research tool. The described technique allows simplifying drastically without loss of stringency the derivation of the key relationships of the theory of spectral analysis of random time series of finite duration and formulating the main correlation identity lying in the basis of the Wiener—Khintchine theorem. It is shown that only a biased estimate of the correlation function, as opposed to an unbiased one, satisfies the main correlation identity and therefore it is the only basis for the possibility of correct application of the Wiener—Khintchine theorem to the real data of finite duration. It is also shown that the appearing undesirable increase in the number of spectral lines in the case of using biased correlation estimates is manifested only inside the subsystem of odd spectrum harmonics and the transition to the even harmonic subsystem eliminates this effect completely. In the case of the general theory of spectra, it is of importance that all the even harmonics coincide with the result of the spectrum direct calculation using the Schuster method, which proves the theoretical equivalence of the direct and indirect methods of the energy spectrum calculation. |
| Starting Page | 247 |
| Ending Page | 262 |
| Page Count | 16 |
| File Format | |
| ISSN | 10231935 |
| Journal | Russian Journal of Electrochemistry |
| Volume Number | 46 |
| Issue Number | 3 |
| e-ISSN | 16083342 |
| Language | English |
| Publisher | SP MAIK Nauka/Interperiodica |
| Publisher Date | 2010-04-14 |
| Publisher Place | Dordrecht |
| Access Restriction | One Nation One Subscription (ONOS) |
| Subject Keyword | random numeric series Wiener—Khintchine theorem correlation function power spectral density Physical Chemistry Electrochemistry |
| Content Type | Text |
| Resource Type | Article |
| Subject | Electrochemistry |
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