## 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

- delay
`tau` for phase space reconstruction (in samples),
- embedding dimension m,
- relative radius r,
- maximum relative shift
`maxdelta` in samples and
- step size (
`stepsize`) in samples.

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]