ABSTRACT

The techniques used to eliminate a measurement noise disrupting a chaotic dataset, wavelet-based techniques are extremely efficient. Wavelet filtering techniques have shown a great efficiency when the impact of the noise on the observations is linear and it is particularly well adapted to spatially inhomogeneous signals. This chapter explains how the wavelet method works in the classical case, why it must be transformed in the chaotic framework and why it should then be rather used in the phase space than in the time domain. The decomposition of a pure and quite smooth function in a wavelet basis to describe it accurately and with few nonzero coefficients. As a consequence, the Daubechies wavelets, which have a compact support, form an interesting class of mother wavelets. The corresponding time series has smaller wavelet coefficients than the observations in the phase space. Fast algorithms calculating wavelet coefficients are based on the dyadic structure of the sample.