Temporal entropy

Description

Compute the entropy of a temporal envelope.

Usage

th(env, breaks)

Arguments

Details

Temporal entropy is calculated according to:

S = -sum(ylogy)/log(N)

with:
y = relative amplitude of the i envelope point,
and

sum(y) = 1

and N = number of envelope points.

Value

A single value varying between 0 and 1 is returned. The value has no unit.

Note

The temporal entropy of a noisy signal with many amplitude modulations will tend towards 1 whereas the temporal entropy of quiet signal will tend towards 0.
Note, however, that a sustained sound with an almost flat envelope will also show a very high temporal entropy except if you compute the entropy on the distribution obtained with the histogram. See examples.

Author(s)

Jerome Sueur, George Zhan for the idea and implementation of the argument breaks.

See Also

sh, csh, H

Examples

# Temporal entropy of a cicada song
data(orni)
envorni<-env(orni,f=22050,plot=FALSE)
th(envorni)
# Smoothing the envelope might slightly change the result.
envorniS<-env(orni,f=22050,smooth=c(50,0),plot=FALSE)
th(envorniS)
# If we mute a part of the cicada song, the temporal entropy decreases
orni2<-mutew(orni,f=22050,from=0.3,to=0.55,plot=FALSE)
envorni2<-env(orni2,f=22050,plot=FALSE)
th(envorni2)
# The temporal entropy of noise tends towards 1
a<-noisew(d=1,f=8000)
enva<-env(a,f=8000,plot=FALSE)
th(enva)
# But be aware that the temporal entropy
# of a sustained sound also tends towards 1
b<-synth(f=8000,d=1,cf=2000,plot=FALSE)
envb<-env(b,f=8000,plot=FALSE)
th(envb)
# except if you use the distribution of the histogram
th(envb, breaks="Sturges")