![harmonic frequency harmonic frequency](https://etap.com/images/default-source/product/harmonic-frequency-scan/impedanceplot.jpg)
We will elaborate how the properties of a signal are represented in the lens of the DFT, and will not discuss whether the DFT is the best method to represent a particular signal. We restrict the frequency-domain analysis method to the Discrete Fourier Transform (DFT), the most classic frequency domain analysis method. In this article, we explain how these harmonics are related to time-domain waveforms. The harmonics can provide additional insight into the underlying neural encoding mechanisms ( O’connell et al., 2015) but their interpretations are not straightforward. For example, when the stimulus rhythm is at f Hz, neural responses can often be observed not just at f but also at its harmonics, i.e., at 2 f, 3 f, 4 f etc. Therefore, some frequency-domain measures may appear unintuitive for researchers mainly using time domain analysis methods. 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. 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). Recently, low-frequency (<3 Hz) neural entrainment has also been observed for abstract stimulus properties such as the rhythms of musical beats and linguistic constituents ( Buiatti et al., 2009 Nozaradan et al., 2011 Ding et al., 2016) and during the processing of natural speech or movies ( Ding and Simon, 2012 Zion Golumbic et al., 2013 Koskinen and Seppä, 2014 Lankinen et al., 2014). Similarly, when the luminance of a visual stimulus, e.g., a Gabor patch, fluctuates at f Hz, a neural response at f Hz can also be observed and is referred to as the steady state visual evoked response (SSVEP Norcia et al., 2015). For example, when the intensity of a sound, e.g., a pure tone, fluctuates at a given frequency ( f Hz), a neural response at that frequency ( f Hz) is often observed and is referred to as the auditory steady state response (aSSR Galambos et al., 1981 Ross et al., 2000 Wang et al., 2012).
![harmonic frequency harmonic frequency](http://4.bp.blogspot.com/-nYY4tMRS93A/TlNGSYG9JtI/AAAAAAAAAPQ/nfmJ1QPTYt0/w1200-h630-p-k-no-nu/Six-Pulse-Converter-Harmonic.jpg)
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.Ĭortical activity, measured by electroencephalography (EEG), magnetoencephalography (MEG), or local field potential recordings (LFP), can synchronize to the rhythm of a sensory stimulus. 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. It is illustrated why neural responses repeating at f Hz do not necessarily generate any neural response at f Hz in the Fourier spectrum. Here, we explain the interpretation of response harmonics, with a special focus on very low-frequency neural entrainment near 1 Hz. However, it is not intuitive how these harmonically related components are related to the response waveform. The Fourier analysis decomposes a periodic signal into harmonically related sinusoids. Low-frequency neural entrainment is often studied using periodically changing stimuli and is analyzed in the frequency domain using the Fourier analysis. 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. 7Neuro and Behavior EconLab, Zhejiang University of Finance and Economics, Hangzhou, Chinaīrain activity can follow the rhythms of dynamic sensory stimuli, such as speech and music, a phenomenon called neural entrainment.6Interdisciplinary Center for Social Sciences, Zhejiang University, Hangzhou, China.5Department of Psychology, New York University, New York, NY, USA.4Neuroscience Department, Max-Planck Institute for Empirical Aesthetics, Frankfurt, Germany.3Department of Neurophysiology, Max-Planck Institute for Brain Research, Frankfurt, Germany.2Department of Neurology, New York University Langone Medical Center, New York, NY, USA.1College of Biomedical Engineering and Instrument Sciences, Zhejiang University, Hangzhou, China.Hong Zhou 1, Lucia Melloni 2,3, David Poeppel 4,5 and Nai Ding 1,6,7*