Filtered point processes tractably capture rhythmic and broadband power spectral structure in neural electrophysiological recordings.

. Neural electrophysiological recordings arise from interacting rhythmic (oscillatory) and broadband (aperiodic) biological subprocesses. Both rhythmic and broadband processes contribute to the neural power spectrum, which decomposes the variance of a neural recording across frequencies. While rhythms in various diseases and brain states continue to be well studied, researchers only recently have systematically studied broadband effects in the power spectrum. Broadband effects include shifts in power across all frequencies, which correlate with changes in local firing rates, and changes in the overall shape of the power spectrum, such as the spectral slope. Shape changes are evident in various conditions and brain states, influenced by factors such as excitation-to-inhibition balance, age, and diseases; additionally, it is increasingly recognized that broadband and rhythmic effects can interact on a sub-second timescale. As such, modeling tools that explicitly deal with both rhythmic and broadband contributors to the power spectrum and capture their interactions are essential to improving the interpretability of power spectral effects.. Here, we introduce a tractable stochastic forward modeling framework designed to capture both narrowband and broadband spectral effects when prior knowledge about the primary biophysical processes involved is available. Population-level neural recordings are modeled as the sum of filtered point processes (FPPs), each representing the contribution of a different biophysical process such as action potentials or postsynaptic potentials.. Our approach builds on prior neuroscience FPP work by allowing multiple interacting processes, time-varying firing rates, and deriving theoretical power spectra and cross-spectra. We demonstrate several properties of the models, including that they divide the power spectrum into frequency ranges dominated by rhythmic and broadband effects and capture spectral effects across multiple timescales, including sub-second cross-frequency coupling.. The framework can interpret empirically observed power spectra and cross-frequency coupling effects in biophysical terms, bridging theoretical models and experimental results.