## Transinformation

Purpose

Description

Tips

Macro Synopsis

Modules

Related Functions

### Purpose

Transinformation of two time series.

### Description

The transinformation of two signals is one of the advanced coupling
measures. Unlike the cross correlation, it takes nonlinear dependencies into
account as well. "Transinformation" yields the information about a random variable
being stochastically dependent on a second variable. Derived from Shannon's
information theory, it is defined by

where denote the phase space densities of the observed
variables.

If the variables are stochastically independent, the transinformation `I`
vanishes. In case of dependencies (even if nonlinear), `I` has a positive
value. Furthermore, you can determine the temporal dependence of the coupling
by varying the relative shift .
Parameters of "Transinformation" are

- delay
`tau` (no. of samples) for phase space reconstruction,
- embedding dimension m,
- relative shift
`delta` of the second signal (as no. of samples),
- minimum relative radius
`rmin`,
- maximum relative radius
`rmax`,
- number n of radius steps

The output signal shows the transinformation as a function of the relative
radius for the phase space search. A plateau in the output graph indicates
the so-called scaling region, i.e. the range of radii where the phase space
reconstruction is best.

Note that since this function operates on 'pure' time series, scales and shifts of the given signals do not affect the result.

### Tips

For a time-resolving computation of the transinformation use

### Macro Synopsis

`y = Transinfo([x1,x2],tau,m,delta,rmin,rmax,n);`

signal x1,x2,y;

int tau,m,delta;

float rmin,rmax;

int n;

### Modules

Nonlinear

### Related Functions

Pointwise transinformation, Conditional coupling divergence (PCCD),
Delta test, Mutual cross information,
Post event scan, Synchronicity histogram.