Denoising Chaotic Signals Using Ensemble Intrinsic Time-Scale Decomposition

Processing chaotic signals is a complicated task due to their nonlinear and non-periodical properties. Conventional linear filters do not allow to properly denoise signals generated by chaotic systems, distorting the carrier while removing the noise, which is critical for such applications as coherent chaotic communications. In this paper, we propose a novel denoising algorithm, called Ensemble Intrinsic Time-Scale Decomposition (EITD) using specific chaotic noise generators. We may use specific chaotic noise generators in the known Ensemble Empirical Mode Decomposition (EEMD), as we also show. Considering the examples of Rössler and Lorenz systems as chaotic waveforms generators, we compare the developed algorithm modifications with other filtration algorithms using ITD and EMD. We use the root-mean-square error (RMSE) as a metric to estimate the denoising quality. Signal-to-noise ratio (SNR) range
$-10 \ldots 20$
dB is examined, and white, pink and chaotic noise generators are utilized to disturb signals under study. As a result, we explicitly show that the developed approach provides the error 2–10 times less in the case of white and pink noise, and is capable of denoising chaotic signals in case of all the considered types of noises, in contrast to Conventional and Iterative ITD and EMD algorithms.