I am following an example provided by MATLAB on 1-D wavelet decomposition (DWT). The number of datapoints is 10000. If we do a level 3 decomposition following a similar example provided by MATLAB using https://www.mathworks.com/help/wavelet/ref/wavedec.html
The length of the coefficients "l" after wavelet decomposition is
[127 127 252 501 1000], corresponding to the length of approximation coefficients at level 3, number of detail coefficients at level 3, number of details coefficients at level 2 and number of detail coefficients at level 1. Why are these numbers not exactly divided by 2?
For example, 1000/2 = 500, it is 501. Similarly at next level 500/2 should be 250 but it is 252 and at the third level 250/2 should be 125 but it is 127.
Secondly, every textbook says that DWT needs 2^n data points. Even if we choose a number such as 8192, the number of decimated coefficients are not exactly and successively divided by 2. What is the reason behind this?