  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.

Neurons and Cognition;Signal Processing