Re: Subband Spectral Entropy

In article <Nu6dnQz_c8zhYw7UnZ2dnUVZ_qPinZ2d@xxxxxxxxxxxx>,
"DWT" <zwfilter09@xxxxxxxxx> wrote:

Yes.

KP


Hello Ken,

Could you please check it out:
http://img10.imageshack.us/img10/4664/49476386kk8.jpg

Why did I get such a result?

This initial signal is divided into the frames (512 samples + 50%
overlap). Applying DWT for each frame (3 decomposition levels), calculating
the entropy on each subband:

Part of Matlab code:
% +1 is required to calculate the entropy for the approximation
coefficients.
% E.g. 3 levels leads to 4 coefficient sets: 3 details (HP filter)
% and 1 approximation (LP filter)

for j=1:decomp_levels+1
ZZZ=length(x);
pdf=(abs(x).^2)./sum(abs(x).^2));
h=pdf.*log2(1./pdf);
ent(j)=sum(h)./log2(ZZZ);
end;

Then I'll just sum(ent) to get the entropy of the current frame.

You suggested to use levels count in the equation [3]. Am I doing right
using the coefficients per each sub-band instead?


I did not notice that you said "calculate the pdf" in your step one.
You need to calculate the power spectral density (PSD). Let's start
from the top...

wi,k is kth sample of the ith subband of the wavelet transform of an
input signal xj.

Then define the DFT of wi,k as

Wi,f=dft(wi,k)

1) Calculate normalized power spectrum as
Qi,f=|Wi,f|^2/|sum(Wi,f)|^2

(#Qi's = # subbands)

2) Transform with the Shannon function:
Hi,f=Qi,f[log(1/Qi,f)]

3) Wavelet spectral entropy:
Ei=sum(Hi,f)/log(Ni) (where Ni is the number of frequency components in
the ith subband)


HTH,

KP
.

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