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:
$$ \boldsymbol{Y}=\frac{\boldsymbol{M} \times \boldsymbol{M}^T}{n} $$
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 $cD_3$ AND $cA_3$?
For example, for a discrete signal that I am applying. It will first generate a $cD_1$ (9x1), $cD_2$ (6x1), $cD_3$ (4x1) and $cA_3$ (4x1).
Each coefficient has a different size.
