Poincare section techniques for speech

When speech signals are modeled as the output of a nonlinear oscillator, a phase space representation can be obtained by combining several delayed versions of the signal into a trajectory in multi-dimensional space. Due to the cyclic nature of voiced speech, the trajectory approximately repeats itself after every pitch period such that at each point in phase space we see a synchronized bundle of trajectories. Cross-sections through these bundles are referred to as Poincare sections and allow us to assess the signal's deviation from strict periodicity. This gives rise to a cyclostationary description of voiced speech. An extra benefit of the Poincare section approach is the possibility for synchronization of pitch cycles during intervals with strongly irregular pitch period.