Interpretations of frequency domain analyses of neural entrainment: Periodicity, fundamental frequency, and harmonics

Hong Zhou, Lucia Melloni, David Poeppel, Nai Ding

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Article number274
JournalFrontiers in Human Neuroscience
StatePublished - Jun 6 2016


  • Harmonics
  • Neural entrainment
  • Oscillations
  • Periodicity
  • Rhythm

ASJC Scopus subject areas

  • Neuropsychology and Physiological Psychology
  • Neurology
  • Psychiatry and Mental health
  • Biological Psychiatry
  • Behavioral Neuroscience


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