Correlation Matrix Problem of Three Decomposition Level of DWT

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Luccas S.
Luccas S. 2024-3-6
I'm trying to apply a DWT with 3 composition levels and the following question arose when calculating the composition matrix. The step I'm trying to follow is:
The DWT coefficientes are obtained from filtering operations and are divided in approximation (cA) and detail coefficients (cD).
Three Decomposition Level of DWT
If a signal f(n) is scaled up to a defined decomposition level, then, it will be producing a wavelet matrix M(J+1,n), this matrix is analysed using its correlation matrix defined by:
where n is the total sample numbers. Therefore, it has a matrix Y(J+1,J+1) which contains the scaled frequency information of the signal.
Each level of decomposition will have a matrix with a different size, so how am I going to analyze the correlation matrix? Should it be done individually? Should I complete with zeros? Should I only analyze cD3 AND cA3?
For example, for a discrete signal that I am applying dwt MATLAB toolbox. It will first generate a cD1 (9x1), cD2 (6x1), cD3 (4x1) and cA3 (4x1).
Each coefficient has a different size.

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