How to obtain Shannon's entropy in specific wavelet packet tree node?

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Nicolò La Porta
Nicolò La Porta 2022-10-4
回答： Sufiyan 2023-5-25
Hi everyone,
I'm trying to extract a subset of features from an ECG signal following some guideline I read in a paper about ECG Wavelet Packet Analysis (WPA).
In this paper the authors use 5 seconds ECG segments and decompose each one of them into eight levels resulting in 510 sub-bands. Then it is written: "The entropy of each sub-band is calculated resulting in a 510 length feature vector. In order to decrease the redundancy of each vector, best wavelet tree is calculated based on Shannon’s criterion. The best tree elements are retained in the original feature vector and the rest of the elements are set to zero."
I managed to calculate the best tree using the besttree(wtp) function but I don't understand how to retain only the best tree elements and put the other to zero. In particular I want to calculate the Shannon's entropy as feature.
Can anyone please help me?

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Sufiyan
Sufiyan 2023-5-25
As you have obtained the best tree using the “besttree()”, the tree obtained will have some non-zero coefficients, which represents the best sub-bands.
The besttree() function calculates the best tree based on the entropy of the wavelet coefficients at each level of the decomposition. If the wavelet coefficients in some sub-bands have low entropy, then those coefficients may not be included in the best tree and will automatically be zero in the final matrix where you are finding the best tree using “besttree()”.
You can find more information about “besttree” in the given below link.
https://www.mathworks.com/help/releases/R2022b/wavelet/ref/wptree.besttree.html
Hope this helps!

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