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Mutual information

Purpose
Description
Macro Synopsis
Modules
Related Functions
References


Purpose

Mutual information

Description

Mutual information is equivalent to Mutual cross information applied to a signal x and a copy of itself. Thus the mutual information of a discrete time series is defined by

where is the probability for the scalar observable to take the value of x1, and is the probability for the observable to take the value x2 after a time delay . is equivalent to the medium amount of information the state x(t) contains about x(t+).

Mutual information operates on a single signal. The parameters are


Due to the dual logarithm in the formula above the output unit is 'bits'.
Note that since this function operates on a 'pure' time series, the scale and the shift of the given signal do not affect the result.

Macro Synopsis

s = MutualInfo(x,tau,m,r,maxdelta,stepsize);
signal x,s;
int tau,m;
float r;
int maxdelta,stepsize;

Modules

Nonlinear

Related Functions

Mutual cross information

References

Shannon/Weaver [45], Liebert/Schuster [9], Fraser/Swinney [47]