I am starting to learn about Wavelets from the book "Wavelet Methods for Time Series Analysis" by Percival and Walden.
To help my understanding, I am trying to use the PyWavelets package to reproduce some of their results for the Daubechies D(4) (=db2) wavelet. In particular I am trying to reproduce the figure on p65 which shows the details, smooths and roughs for the series with 16 elements:
[ 0.2 -0.4 -0.6 -0.5 -0.8 -0.4 -0.9 0. -0.2 0.1 -0.1 0.1 0.7 0.9
I see that in Pywavelets the filter bank coefficients are in the reverse order to those in Percival and Walden. Also, the details I obtain using pywt.dwt are different from the values given in the book. Even taking this into account, I am still getting different results.
It seems that the algorithms are slightly different.
Is the precise algorithm used in pywt.dwt documented in the literature anywhere?