Discrete wavelet transform behaves like identity

[ThomasChaffey]

Apologies if I am missing something very basic (I am only just learning about wavelets), but I believe there is a bug in dwt:

n = 2^6 - 1
u = cos.(2*pi*range(0, stop=1, length=n))
wav = wavelet(WT.haar) # also tested WT.db2
w = dwt(u, wav)
display(w == u)

This code returns true. Expected behaviour is that w is the discrete wavelet transform of u, something like I get running the same experiment in Mathematica.

Version info:

Wavelets 0.9.4
Julia 1.6.3

[JeffFessler]

I can confirm seeing the same with Julia 1.7.3.
Changing the first line to n = 2^6 leads to output that makes more sense (I didn't check the values).
Typing ]?dwt might help you see the issue.
The default value of L (# of transform levels) is maxtransformlevels(x) which is 0 for your signal because its length has no factors of 2.
It is not a bug, but rather a limitation (or design choice) of the implementation here.
The same example in Matlab returns two vectors of length 32, meaning that it must be padding somehow, according to the dtwmode setting apparently.
You should decide what kind of padding you want. See related issue #80.

[ThomasChaffey]

Wonderful, thank you! Setting n = 2^6 does indeed solve the problem, the output is as expected now.