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Approximate entropy (ApEn) as a complexity measure
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28.The reason that correlation dimension is 0, not 1 for is that the sampling frequency of the sine function is commensurate with π, so that the phase space realization from the sine function is a discrete point set. If we choose a sampling frequency incommensurate with π in the sine component of the MIX definition, the correlation almost surely for and the difficulty remains—the correlation dimension fails to discriminate members of this process from one another.
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30.A family of ε estimators for ApEn(m,r) is proposed in Ref. 11 to achieve bias reduction.
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