Algorithm for dwt

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James Housden

Dec 30, 2021, 12:26:48 PM12/30/21
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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
  0.   0.3].
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?

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