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Details for article 8 of 30 found articles
| Title: |
Cycles determination |
| Author: |
De Prins, J. Bovy, C. Cornelissen, G. Gillard, R. |
| Appeared in: |
Biological rhythm research |
| Paging: | Volume 3 (1972) nr. 3-4 pages 327-328 |
| Year: |
1972-12 |
| Contents: |
Cycle determination, i.e. research and detection of quasi monochromatic signals, is certainly not an easy task. Indeed, there are numerous mathematical, or less mathematical, methods proposed for this purpose. However, pitfalls in applications are nearly as numerous as the proposed methods. This is due to the fact that the main procedures require mathematical properties which are not fulfilled in reality by the users, for example stationarity, ergodicity, infinite time of observation (Bendat et al., 1971). On the other hand, the main spectral methods are focused on the amplitude of the power spectrum. This means that all the phase information is lost in the process. Another danger is a too sophisticated mathematical handling, creating periodicities due to the filtering of the data by the procedure itself (Slutzky, 1937). We introduced a method, which as we believe, is free from those drawbacks. We proceed as follows: We define the number of degrees of freedom N of the studied function f(t) following Gabor's procedure in information theory: N = 2 JA T where JA is the cut-off frequency and T the total time of observation. The finite number of degrees of freedom means that the determination of N equidistant values of f(t) gives us a complete knowledge of this function. It also means that the spectrum will be defined by a discrete set of N/2 terms, each term being characterized by two figures (amplitude and phase, for example). We divide the time of observation in R equal intervals. We calculate the complex discrete Fourier transform (D.F.T.) of each interval by means of the F.F.T. algorithm. We study the phase coherence between the coefficients of the consecutive Fourier transform as well as the spectrum computed by taking the average of the R spectra. Phase coherence indicates the presence of a signal, and allows precise frequency determination. Partial coherence is characteristic for a slowly fluctuating phenomenon with respect of T. Absence of coherence is typical for a random noise origin. A detectability level is determined from the statistics of phase and amplitude and gives the upper amplitude limit for undetectable signals. If a signal of a given frequency is suspected, a shift may be applied in the Fast Fourier Transform for confirmation or invalidation. This method was applied successfully to different studies (transistor's noise, atmospheric pressure, sunspots, ants) for which cycles were found. On the other hand, the same procedure shows a lack of periodicities on Lake Saki varves and dendrochronological data. The method we use was described in 1971 (De Prins et al., 1971). A brief summary of this method and a complete description of its application to cycle determination will be published in the Journal of Interdisciplinary Cycle Research (probably volume 4). The shape of the signal may be measured by signal averaging techniques (De Prins et al., 1971). |
| Publisher: |
Taylor & Francis |
| Source file: |
Elektronische Wetenschappelijke Tijdschriften |
Details for article 8 of 30 found articles
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