Time-frequency analysis using damped-oscillator pseudo-wavelets: Application to electrophysiological recordings.

The damped-oscillator pseudo-wavelet is presented as a method of time-frequency analysis along with a new spectral density measure, the data power. An instantaneous phase can be defined for this pseudo-wavelet, and it is easily inverted. The data power measure is tested on both computer generated data and in vivo intrahippocampal electrophysiological recordings from a rat. The data power spectral density is found to give better time and frequency resolution than the more conventional total energy measure, and additionally shows intricate time-frequency structure in the rat that is altered in association with the emergence of epilepsy. With epileptogenesis, the baseline theta oscillation is severely degraded and is absorbed into a broader gamma band. There are also broad 600 Hz and 2000 Hz bands which localize to hippocampal layers that are distinct from those of the theta and gamma bands. The 600 Hz band decreases in prominence with epileptogenesis while the 2000 Hz band increases in prominence. The origins of these high frequency bands await further study. In general, we find that the damped-oscillator pseudo-wavelet is easy to use and is particularly suitable for problems where a wide range of oscillator frequencies is expected.