Oscillatory data analysis using the extended Hilbert transform method

Oscillatory phenomena are observed in various biological systems, such as spinal nervous systems and circadian rhythms. These macroscopic oscillatory phenomena appear as a result of synchronization of microscopic oscillators, such as pacemaker cells. The first step in the analysis of synchronization is to reconstruct the "phase" from the observed signal. The Hilbert transform method is one of the popular methods for phase reconstruction, but it is known that it can only accurately reconstruct the phase from a limited class of signals such as narrowband signals. In this study, we show that the Hilbert transform method has a low-pass filter-like effect on the phase modulation and propose an "extended Hilbert transform method" that can be applied to a wider class of signals.

In this talk, I will introduce the extended Hilbert transform method, and its application to phase shift detection and coupling network inference.