Time-Frequency Domain Analogues of Phase Space Sub-Planck Structures

Measuring sub-Planck structural analogues in chronocyclic phase space

Phase space quasi-probability distributions of certain quantum states reveal structure on a scale that is small compared to the Planck area. Using an analog between the wavefunction of a single photon and the electric field of a classical ultrashort optical pulse we show that spectral shearing interferometry enables measurement of such structure directly, thereby extending an idea of Krzysztof ...

Frequency Sweeping of Phase Space Structures

Holes and clumps, spontaneously formed in the nonlinear development of a single mode driven by a weakly destabilizing kinetic distribution function in a dissipative medium, were expected to persist for an appropriate collisional time scale. However, Fokker-Planck calculations for the nonlinear system abruptly break down in the course of the calculation for some initial conditions. We nd that th...

From phase space to frequency domain: a time-frequency analysis for chaotic time series.

Time-frequency analysis is performed for chaotic flow with a power spectrum estimator based on the phase-space neighborhood. The relation between the reference phase point and its nearest neighbors is demonstrated. The nearest neighbors, representing the state recurrences in the phase space reconstructed by time delay embedding, actually cover data segments with similar wave forms and thus poss...

Newborn EEG Seizure Detection Based on Interspike Space Distribution in the Time-Frequency Domain

This paper presents a new time-frequency based EEG seizure detection method. This method uses the distribution of interspike intervals as a criterion for discriminating between seizure and nonseizure activities. To detect spikes in the EEG, the signal is mapped into the time-frequency domain. The high instantaneous energy of spikes is reflected as a localized energy in time-frequency domain. Hi...

Teleportation fidelity as a probe of sub-Planck phase-space structure