Fabus, M. S. | Search bioRxiv

bioRxiv2021

Understanding Harmonic Structures Through Instantaneous Frequency

The analysis of harmonics and non-sinusoidal waveform shape in neurophysiological data is growing in importance. However, a precise definition of what constitutes a harmonic is lacking. In this paper, we propose a rigorous definition of when to consider signals to be in a harmonic relationship based on an integer frequency ratio, constant phase, and a well-defined joint instantaneous frequency. We show this definition is linked to extrema counting and Empirical Mode Decomposition (EMD). We explore the mathematics of our definition and link it to results from analytic number theory. This naturally leads to us to define two classes of harmonic structures, termed strong and weak, with different extrema behaviour. We validate our framework using both simulations and real data. Specifically, we look at the harmonics structure in the FitzHugh-Nagumo model and the non-sinusoidal hippocampal theta oscillation in rat local field potential data. We further discuss how our definition helps to address mode splitting in EMD. A clear understanding of when harmonics are present in signals will enable a deeper understanding of the functional and clinical roles of non-sinusoidal neural oscillations.

neuroscience↗

bioRxiv2021

Automatic decomposition of electrophysiological data into distinct non-sinusoidal oscillatory modes

Neurophysiological signals are often noisy, non-sinusoidal, and consist of transient bursts. Extraction and analysis of oscillatory features (such as waveform shape and cross-frequency coupling) in such datasets remains difficult. This limits our understanding of brain dynamics and its functional importance. Here, we develop Iterated Masking Empirical Mode Decomposition (itEMD), a method designed to decompose noisy and transient single channel data into relevant oscillatory modes in a flexible, fully data-driven way without the need for manual tuning. Based on Empirical Mode Decomposition (EMD), this technique can extract single-cycle waveform dynamics through phase-aligned instantaneous frequency. We test our method by extensive simulations across different noise, sparsity, and non-sinusoidality conditions. We find itEMD significantly improves the separation of data into distinct non-sinusoidal oscillatory components and robustly reproduces waveform shape across a wide range of relevant parameters. We further validate the technique on multi-modal, multi-species electrophysiological data. Our itEMD extracts known rat hippocampal theta waveform asymmetry and identifies subject-specific human occipital alpha without any prior assumptions about the frequencies contained in the signal. Notably, it does so with significantly less mode mixing compared to existing EMD-based methods. By reducing mode mixing and simplifying interpretation of EMD results, itEMD will enable new analyses into functional roles of neural signals in behaviour and disease. New & NoteworthyWe introduce a novel, data-driven method to identify oscillations in neural recordings. This approach is based on Empirical Mode Decomposition and reduces mixing of components, one of its main problems. The technique is validated and compared with existing methods using simulations and real data. We show our method better extracts oscillations and their properties in highly noisy and non-sinusoidal datasets. Running HeadDecomposition of data into non-sinusoidal oscillatory modes

neuroscience↗