Real-time estimation of phase and amplitude with application to neural data

Computation of the instantaneous phase and amplitude via the Hilbert Transform is a powerful tool of data analysis. This approach finds many applications in various science and engineering branches but is not proper for causal estimation because it requires knowledge of the signal's past and future. However, several problems require real-time estimation of phase and amplitude; an illustrative example is phase-locked or amplitude-dependent stimulation in neuroscience. In this paper, we discuss and compare three causal algorithms that do not rely on the Hilbert Transform but exploit well-known physical phenomena, the synchronization and the resonance. After testing the algorithms on a synthetic data set, we illustrate their performance computing phase and amplitude for the accelerometer tremor measurements and a Parkinsonian patient's beta-band brain activity.

Automated summary

The computation of instantaneous phase and amplitude using the Hilbert Transform is a powerful tool in data analysis, however, it is not suitable for causal estimation due to the requirement of knowledge of past and future signals. Real-time estimation of phase and amplitude is important in various fields, such as neuroscience. Three causal algorithms that do not rely on the Hilbert Transform but utilize synchronization and resonance were discussed and compared in this study, with their performance tested on synthetic data and accelerometer tremor measurements as well as Parkinsonian patient's brain activity.