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Neural oscillations are widely studied using methods based on the Fourier transform, which models data as sums of sinusoids. This has successfully uncovered numerous links between oscillations and cognition or disease. However, neural data are nonsinusoidal, and these nonsinusoidal features are increasingly linked to a variety of behavioral and cognitive states, pathophysiology, and underlying neuronal circuit properties. Here, we present a new analysis framework-one that is complementary to existing Fourier- and Hilbert-transform based approaches-that quantifies oscillatory features in the time domain, on a cycle-by-cycle basis. We have released this cycle-by-cycle analysis suite as bycycle, a fully documented, open-source Python package with detailed tutorials and troubleshooting cases. This approach performs tests to assess whether an oscillation is present at any given moment and, if so, quantifies each oscillatory cycle by its amplitude, period, and waveform symmetry, the latter of which is missed using conventional approaches. In a series of simulated event-related studies, we show how conventional Fourier- and Hilbert-transform approaches can conflate event-related changes in oscillation burst duration as increased oscillatory amplitude and as a change in the oscillation frequency, even though those features were unchanged in simulation. Our approach avoids these errors. Further, we validate this approach in simulation and against experimental recordings of patients with Parkinson's disease, who are known to have nonsinusoidal beta (12-30 Hz) oscillations. 

It is widely assumed that distributed neuronal networks are fundamental to the functioning of the brain. Consistent spike timing between neurons is thought to be one of the key principles for the formation of these networks. This can involve synchronous spiking or spiking with time delays, forming spike sequences when the order of spiking is consistent. Finding networks defined by their sequence of time-shifted spikes, denoted here as spike timing networks, is a tremendous challenge. As neurons can participate in multiple spike sequences at multiple between-spike time delays, the possible complexity of networks is prohibitively large. We present a novel approach that is capable of (1) extracting spike timing networks regardless of their sequence complexity, and (2) that describes their spiking sequences with high temporal precision. We achieve this by decomposing frequency-transformed neuronal spiking into separate networks, characterizing each network’s spike sequence by a time delay per neuron, forming a spike sequence timeline. These networks provide a detailed template for an investigation of the experimental relevance of their spike sequences. Using simulated spike timing networks, we show network extraction is robust to spiking noise, spike timing jitter, and partial occurrences of the involved spike sequences. Using rat multi-neuron recordings, we demonstrate the approach is capable of revealing real spike timing networks with sub-millisecond temporal precision. By uncovering spike timing networks, the prevalence, structure, and function of complex spike sequences can be investigated in greater detail, allowing us to gain a better understanding of their role in neuronal functioning. 

Neural oscillations are ubiquitous across recording methodologies and species, broadly associated with cognitive tasks, and amenable to computational modelling that investigates neural circuit generating mechanisms and neural population dynamics. Because of this, neural oscillations offer an exciting potential opportunity for linking theory, physiology and mechanisms of cognition. However, despite their prevalence, there are many concerns—new and old—about how our analysis assumptions are violated by known properties of field potential data. For investigations of neural oscillations to be properly interpreted, and ultimately developed into mechanistic theories, it is necessary to carefully consider the underlying assumptions of the methods we employ. Here, we discuss seven methodological considerations for analysing neural oscillations. The considerations are to (1) verify the presence of oscillations, as they may be absent; (2) validate oscillation band definitions, to address variable peak frequencies; (3) account for concurrent non‐oscillatory aperiodic activity, which might otherwise confound measures; measure and account for (4) temporal variability and (5) waveform shape of neural oscillations, which are often bursty and/or nonsinusoidal, potentially leading to spurious results; (6) separate spatially overlapping rhythms, which may interfere with each other; and (7) consider the required signal‐to‐noise ratio for obtaining reliable estimates. For each topic, we provide relevant examples, demonstrate potential errors of interpretation, and offer suggestions to address these issues. We primarily focus on univariate measures, such as power and phase estimates, though we discuss how these issues can propagate to multivariate measures. These considerations and recommendations offer a helpful guide for measuring and interpreting neural oscillations.