Decomposition

We transform Ligeti's Etude no.4, Book 1 so that its global pitch dynamics become continuous. For this we wavelet transform the pitch sequence of Ligeti's Etude using Daubechies 8 wavelet. The decomposition is done at 7 levels.
After decomposing the signal we perform a 4-dimensional state-space reconstruction of the largest scale approximation and rotate it by PI radians on each of the six rotation planes.
We then project the rotated trajectory back to a single dimension and inverse wavelet transform it to recover the complete pitch sequence of the Etude. Because the Daubechies 8 wavelet is smooth, the approximation is smooth as well.

Ligeti's piano Etude no.4, Book 1.

Ligeti's piano Etude no.4, Book 1 transformed by rotating the lag-space of the 7th scale approximation of the pitch sequence using Daubechies 8 wavelet.