title: Interpretations of Frequency Domain Analyses of Neural Entrainment: Periodicity, Fundamental Frequency, and Harmonics.
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.
authors.affiliation: College of Biomedical Engineering and Instrument Sciences, Zhejiang University Hangzhou, China.
authors.forename: Hong
authors.initials: H
authors.lastname: Zhou
authors.affiliation: Department of Neurology, New York University Langone Medical CenterNew York, NY, USA; Department of Neurophysiology, Max-Planck Institute for Brain ResearchFrankfurt, Germany.
authors.forename: Lucia
authors.initials: L
authors.lastname: Melloni
authors.affiliation: Neuroscience Department, Max-Planck Institute for Empirical AestheticsFrankfurt, Germany; Department of Psychology, New York UniversityNew York, NY, USA.
authors.forename: David
authors.initials: D
authors.lastname: Poeppel
authors.affiliation: College of Biomedical Engineering and Instrument Sciences, Zhejiang UniversityHangzhou, China; Interdisciplinary Center for Social Sciences, Zhejiang UniversityHangzhou, China; Neuro and Behavior EconLab, Zhejiang University of Finance and EconomicsHangzhou, China.
authors.forename: Nai
authors.initials: N
authors.lastname: Ding
keywords: harmonics; neural entrainment; oscillations; periodicity; rhythm