Time-scale (wavelet)

Entropies.TimeScaleMODWT — Type

TimeScaleMODWT <: WaveletProbabilitiesEstimator

Apply the maximal overlap discrete wavelet transform (MODWT) to a signal, then compute probabilities/entropy from the energies at different wavelet scales. This implementation is based on Rosso et al. (2001)^[Rosso2001].

TimeScaleMODWT(wl::Wavelets.WT.OrthoWaveletClass = Wavelets.WT.Daubechies{12}())

Construct a TimeScaleMODWT probabilities/entropy estimator with wavelet wl.

Example

Manually picking a wavelet is done as follows.

using Entropies, Wavelets
wl = Wavelets.WT.Daubechies{4}()
est = TimeScaleMODWT(wl)

# output

TimeScaleMODWT(Wavelets.WT.Daubechies{4}())

If no wavelet provided, the default is Wavelets.WL.Daubechies{12}()).

using Entropies, Wavelets
est = TimeScaleMODWT()

# output

TimeScaleMODWT(Wavelets.WT.Daubechies{12}())

source

Example

The scale-resolved wavelet entropy should be lower for very regular signals (most of the energy is contained at one scale) and higher for very irregular signals (energy spread more out across scales).

using Entropies, PyPlot
N, a = 1000, 10
t = LinRange(0, 2*a*π, N)

x = sin.(t);
y = sin.(t .+  cos.(t/0.5));
z = sin.(rand(1:15, N) ./ rand(1:10, N))

est = TimeScaleMODWT()
h_x, h_y, h_z = genentropy(x, est), genentropy(y, est), genentropy(z, est)

f = figure(figsize = (10,6))
ax = subplot(311)
px = plot(t, x; color = "C1", label = "h=$(h=round(h_x, sigdigits = 5))");
ylabel("x"); legend()
ay = subplot(312)
py = plot(t, y; color = "C2", label = "h=$(h=round(h_y, sigdigits = 5))");
ylabel("y"); legend()
az = subplot(313)
pz = plot(t, z; color = "C3", label = "h=$(h=round(h_z, sigdigits = 5))");
ylabel("z"); xlabel("Time"); legend()
tight_layout()
savefig("waveletentropy.png")

Rosso2001Rosso, O. A., Blanco, S., Yordanova, J., Kolev, V., Figliola, A., Schürmann, M., & Başar, E. (2001). Wavelet entropy: a new tool for analysis of short duration brain electrical signals. Journal of neuroscience methods, 105(1), 65-75.