# Sub-band partitioning of filter-banks

In ECE-700 Filterbank Notes the partitioning is $\Delta = \frac{2\pi}{M}$ with center-frequencies at $\omega_k = \frac{2\pi}{M}k$ which makes me wonder, considering that frequencies in the range from $\pi$ to $2\pi$ are just the negative versions of the range from $0$ to $\pi$, which divide into low- and high-pass frequencies.

In the follow-up picture the partitioning then stretches from $0$ to $\pi$ - is there someone so nice as to explain to me what I'm not understanding here?

The notes made me wonder as well, and I cannot suspect the author made a mistake. The first graph with periodicity is generic. The second one corresponds to dyadic iteration (wavelets), often displayed in $[0,\pi]$, except when dealing with complex wavelets where $[-\pi,\pi]$ is used. I agree, $[0,2\pi]$ could have been used instead, but I have never seen the $2^k$ partitioning mirrored at the end.
You can see from the rest of the paper that the author uses $[0,\pi]$.