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renyi

Measure Renyi information

Calling Sequence

R = renyi(TFR)
R = renyi(TFR, T)
R = renyi(TFR, T, F)
R = renyi(TFR, T, F, ALPHA)

Parameters

TFR :

M by N array: the 2-D density function (or mass function). Eventually TFR can be a time-frequency representation, in which case its first row must correspond to the lower frequencies.

T :

a real vector of size N: the abscissa vector parametrizing the TFR matrix. T can be a non-uniform sampled vector (eventually a time vector)(default : (1:N)).

F :

a real vector of size M: the ordinate vector parametrizing the TFR matrix. F can be a non-uniform sampled vector (eventually a frequency vector) (default : (1:M)).

ALPHA :

a positive scalar: the rank of the Renyi measure (default : 3).

R :

the alpha-rank Renyi measure (in bits if TFR is a time-frequency matrix) : R=log2[Sum[TFR(Fi,Ti)^ALPHA dFi.dTi]/(1-ALPHA)]

Description

renyi measures the Renyi information relative to a 2-D density function TFR (which can be eventually a TF representation).

The Renyi entropy furnishes measures for estimating signal information and complexity in the time–frequency plane. When applied to a TFR from the Cohen’s or the affine classes, the Renyi entropies conform to the notion of complexity that we use when inspecting time–frequency images.

Examples

s = atoms(64,[32,.3,16,1]);
[TFR,T,F] = tfrsp(s);
R = renyi(TFR,T,F,3)

s = atoms(64,[16,.2,10,1;40,.4,12,1]);
[TFR,T,F] = tfrsp(s);
R = renyi(TFR,T,F,3)

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