On self-repeating effect in reconstruction of irregular waves

Abstract

The paper is focused on the previously known effect of "statistical self-repetition" encountered when a wave record is reconstructed from spectrum with a constant frequency step. A correlation function calculated for such a record shows a repetitive pattern of high values. It means an unrealistically strong probabilistic dependence between certain time sections of the process. The effect remains even if the autocorrelation function is calculated directly from spectrum without actual reconstruction of the wave record. An attempt to work the effect around using a variable frequency step leads to a spread of the error. It appears as a series of unrealistically high values instead of discrete peaks. The previous work of the author also found that the presence or absence of the effect strongly depends on the method of numerical integration. The paper concludes that the nature of this effect is a numerical error caused by the highly oscillatory character of an integrand in cosine Fourier transform for large values of time. The paper also discusses the practical implications of this conclusion and is based on earlier publications (Belenky 1994, 1995). © Springer Science+Business Media B.V. 2011.