Differences between $\tt wentropy$ in MATLAB and entropy definition

MATLAB offer's a Shannon entropy calculation in its wavelet package:

$$H(X) = -\sum_{i=0}^{N-1} x_i^2\log(x_i^2)$$

I'm wondering what this formula means, since it has no relation with the probabilities of the symbols in the sequence $x$. It is closer to Spectral Entropy (in the domain of $x$)...

• The documentation for that function (mathworks.com/help/wavelet/ref/wentropy.html) is wrong, at least concerning Shannon entropy. A signal has no entropy. – MBaz Oct 27 '16 at 12:55
• @MBaz this is what I thought... But it is MATLAB!! Spectral Entropy is defined for the PSD of a signal, which is an orthonormal transformation of the signal and the documentation says that the entropy is calculated over the components of the signal in an orthonormal basis... Anyway, I'm quite confused.... – ignatius Oct 27 '16 at 14:59
• My only guess is that in the wavelets field they use a different definition of entropy, and they overload "Shannon entropy" because the formula has the same form. – MBaz Oct 27 '16 at 17:16
• I vote asking MATLAB team directly... I'll let you know – ignatius Oct 27 '16 at 17:30