Entropy analysis of noise contaminated signals
J. Freund
Inst. of Physics, Humboldt University Berlin, Germany
The regularities within a signal, e.g. the periodic
components, can be detected using standard statistical tools like
power spectrum. Dynamical entropies reflect structure within a signal
in a wider sense. For their application one needs a conversion of a
time/state-continuous signal to a time/state-discrete one, involving
sampling and coarse graining techniques. At the order/chaos
transition, e.g. period doubling accumulation point or
quasi-periodicity, one thus may yield self similar symbol sequences.
Long-range correlations are reflected by a characteristic scaling law
valid for certain conditional entropies. The question arises whether
these correlations survive some noise affecting the signal, hence,
contaminating the pure structure. Noise is assumed to independently
(white noise) flip symbols of the sequence with probability
. We will show that in the weak noise limit 
the subexponential scaling law of conditional entropies will sustain
this perturbation.