Wavelet analysis of a Gaussian Kolmogorov signal
Massimo Vergassola, Roberto Benzi, Luca Biferale, Dmitri Pisarenko · Journal of Physics A Mathematical and General · 1993
Several attempts have been made recently to use wavelets transforms for extracting histograms of scaling exponents from experimental turbulence data. Similar techniques are here applied to a Gaussian signal having a Kolmogorov 5 / 3 energy spectrum. This is an instance of the class of fractional Brownian motions, having scaling exponent 1 / 3 almost everywhere. For the Gaussian signal, a spurious non-trivial histogram is obtained by applying a Mexican hat wavelet transform analysis. On the other hand, we show that the use of complex wavelets and, even more so, the application of an optimal wavelet transform method strongly reduce the spurious fluctuations observed in the processing of the Gaussian signal.