sh {seewave}

Shannon and Renyi spectral entropy

Description

This function computes the Shannon or Renyi entropy of a frequency spectrum

Usage

sh(spec, alpha = "shannon")

Arguments

spec

a data set resulting of a spectral analysis obtained with spec or meanspec (not in dB).

alpha

a character string, by default "shannon" to compute Shannon entropy, "simpson" to compute Simpson entropy otherwise a numeric vector of length 1 with a value superior to 0 but different to 1 to compute Renyi entropy. See the examples.

Details

. Shannon spectral entropy is calculated according to:

S = -\frac{\sum_{i = 1}^{N} y_i log_2(y_i)}{log_2(N)}

. Simpson or Gini-Simpson spectral entropy (or index) is computed according to:

GS = 1 - \sum_{i=1}^{N} y_{i}^2

. Renyi spectral entropy of order alpha is calucalted according to:

R = \frac{1}{1-\alpha} \times log_2(\sum_{i = 1}^{N} y_{i}^{\alpha})

with

\alpha \geq 0

\alpha \neq 1

y = relative amplitude of the i frequency,

\sum_{i = 1}^{N} y_i = 1

and N = number of frequencies.

Value

A numeric vector of length 1 is returned. The value has no unit.

Note

The Shannon entropy scaled between 0 and 1 is also known as Pielou's evenness index

Note

The Shannon spectral entropy of a noisy signal will tend towards 1 whereas the Shannon spectral entropy of a pure tone signal will tend towards 0. See Han et al. for details regarding the Renyi entropy.

Author(s)

Jerome Sueur and Laurent Lellouch

References

Han, NC, Muniandy SV, Dayou J (2011) Acoustic classification of Australian anurans based on hybrid spectral-entropy approach. Applied Acoustics.

Nunes RR, Almeida de MP, Sleigh JW (2004) - Spectral entropy: a new method for anesthetic adequacy. Revista Brasileira de Anestesiologia, 54, 413-422.

Renyi A (1961) - On measures of information and entropy. Proceedings of the 4th Berkeley Symposium on Mathematics, Statistics and Probability 1960. pp. 547-561.

Simpson EH (1949) - Measurement of diversity. Nature, 163, 688.

See Also

csh,th, H, sfm

Examples

a<-synth(f=8000,d=1,cf=2000,plot=FALSE)
speca<-spec(a,f=8000,at=0.5,plot=FALSE)
## Shannon spectral entropy
sh(speca)
# [1] 0.2336412
b<-noisew(d=1,f=8000)
specb<-spec(b,f=8000,at=0.5,plot=FALSE)
sh(specb)
# close to 1
## Renyi spectral entropy
sh(speca, alpha=2)
sh(speca, alpha=3)