Real-time phase and amplitude estimation of neurophysiological signals exploiting a non-resonant oscillator

A recent advancement in the field of neuromodulation is to adapt stimulation parameters according to pre-specified biomarkers tracked in real-time. These markers comprise short and transient signal features, such as bursts of elevated band power. To capture these features, instantaneous measures of phase and/or amplitude are employed, which inform stimulation adjustment with high temporal specificity. For adaptive neuromodulation it is therefore necessary to precisely estimate a signal's phase and amplitude with minimum delay and in a causal way, i.e. without depending on future parts of the signal. Here we demonstrate a method that utilizes oscillation theory to estimate phase and amplitude in real-time and compare it to a recently proposed causal modification of the Hilbert transform. By simulating real-time processing of human LFP data, we show that our approach almost perfectly tracks offline phase and amplitude with minimum delay and is computationally highly efficient.