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Example waveforms
Example waveform shapes

Electrophysiological recordings of neuronal activity show spontaneous and task-dependent changes in their frequency-domain power spectra. These changes are conventionally interpreted as modulations in the amplitude of underlying oscillations. However, on a single cycle level, there is a rich set of dynamics that could lead to such time or trial averaged differences. We utilise methods such as the Empirical Mode Decomposition and Hidden Markov Modelling to gain insight into these underlying dynamics.

The Empirical Mode Decomposition (EMD) allows for analyses of oscillatory frequency at a very high temporal resolution, even detecting subtle changes in instantaneous frequency within single cycles of an oscillation. We have shown that the instantaneous frequency profile of a cycle provides a detailed readout of its time-domain waveform shape whilst correcting for any differences in amplitude, timing, or duration between cycles.

Another related possibility is that transient spectral ‘bursts’ underly averaged neuronal spectra. These events can be modelled as state dynamics in a Hidden Markov Model allowing subsequent analyses to map to changes in trial-average spectral power into changes in burst amplitude, bust duration and burst interval.
 
References
  1. Andrew J. Quinn, Vítor Lopes-dos-Santos, Norden Huang, Wei-Kuang Liang, Chi-Hung Juan, Jia-Rong Yeh, Anna C. Nobre, David Dupret & Mark W. Woolrich (April:2021) Within-cycle instantaneous frequency profiles report oscillatory waveform dynamics bioRxiv, 2021.04.12.439547 https://www.doi.org/10.1101/2021.04.12.439547.
  2. Quinn, Andrew J., van Ede, Freek., Brookes, Matthew J., Heideman, Simone G., Nowak, Magdalena., Seedat, Zelekha A., Vidaurre, Diego., Zich, Catharina., Nobre, Anna C. & Woolrich, Mark W (November:2019) Unpacking Transient Event Dynamics in Electrophysiological Power Spectra Brain Topography, 32, 1020--1034 https://www.doi.org/10.1007/s10548-019-00745-5.
  3. van Ede, Freek., Quinn, Andrew J., Woolrich, Mark W. & Nobre, Anna C (July:2018) Neural Oscillations: Sustained Rhythms or Transient Burst-Events? Trends in Neurosciences, 41, 415--417 https://www.doi.org/10.1016/j.tins.2018.04.004.