Abstract
Brain activity can follow the rhythms of dynamic sensory stimuli, such as speech and music, a phenomenon called neural entrainment. It has been hypothesized that low-frequency neural entrainment in the neural delta and theta bands provides a potential mechanism to represent and integrate temporal information. Low-frequency neural entrainment is often studied using periodically changing stimuli and is analyzed in the frequency domain using the Fourier analysis. The Fourier analysis decomposes a periodic signal into harmonically related sinusoids. However, it is not intuitive how these harmonically related components are related to the response waveform. Here, we explain the interpretation of response harmonics, with a special focus on very low-frequency neural entrainment near 1 Hz. It is illustrated why neural responses repeating at f Hz do not necessarily generate any neural response at f Hz in the Fourier spectrum. A strong neural response at f Hz indicates that the time scales of the neural response waveform within each cycle match the time scales of the stimulus rhythm. Therefore, neural entrainment at very low frequency implies not only that the neural response repeats at f Hz but also that each period of the neural response is a slow wave matching the time scale of a f Hz sinusoid.
Highlights
Cortical activity, measured by electroencephalography (EEG), magnetoencephalography (MEG), or local field potential recordings (LFP), can synchronize to the rhythm of a sensory stimulus
It has been hypothesized that low-frequency neural synchronization to a stimulus provides a mechanism for selective attention and temporal integration of information (Schroeder et al, 2008; Schroeder and Lakatos, 2009; Giraud and Poeppel, 2012), and is important for parsing the temporal structure of speech and music (Nozaradan et al, 2011; Ding et al, 2016)
Neural entrainment to a stimulus rhythms is often analyzed in the frequency domain, while traditional neurophysiological responses, e.g., the event-related responses, are usually analyzed in the time domain
Summary
Cortical activity, measured by electroencephalography (EEG), magnetoencephalography (MEG), or local field potential recordings (LFP), can synchronize to the rhythm of a sensory stimulus. The article is organized as follows: we first present examples that describe the relationship between time-domain signal periodicity and signal spectrum. Since it remains controversial whether the experimentally observed neural tracking of such low-frequency stimulus rhythms reflects a succession of eventrelated responses or a proper entrainment of neural oscillators (Ding and Simon, 2014; Keitel et al, 2014). We describe how to interpret the power spectrum of a series of eventrelated responses These discussions are purely based on intuitive examples, avoiding a more formal, mathematical treatment (for formal treatment, see, e.g., Oppenheim et al, 1989).
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