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

TL;DR

This paper introduces and compares three causal algorithms for real-time estimation of phase and amplitude in signals, crucial for applications like neural stimulation, avoiding the non-causal Hilbert Transform.

Contribution

The paper presents novel causal algorithms based on synchronization and resonance phenomena for real-time phase and amplitude estimation in neural data.

Findings

Algorithms perform well on synthetic data

Effective in real neural and tremor data

Outperform traditional non-causal methods

Abstract

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.