Wavelet analysis of the Voyager data on planetary rings. I. Description of the method
In this paper we present a new method which allows us to extract signal
from low (of the order of 1) signal to noise ratio data. The
noise is almost completely removed, and the significance of the
resulting signal is quantified against pure chance fluctuations. The
technique is based on a wavelet transform, and uses a crude
pattern--recognition algorithm in the space--scale plane to extract
the interesting information. This method has been applied to
simulated signals with signal to noise ratio ranging from 0.4 to 2.
and the reconstructed signals are shown. From the wavelet transform
coefficients, it is possible to gain some quantitative information
on the size of the detected structures. As a first real case
application, we present the analysis of the Encke gap ringlet in the
Saturn's rings. We show that its detailed shape contain at least two
peaks, and that its total width is about 8 km, while the width of
the left peak is about 1.5 km.