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Figure 1 | Journal of Circadian Rhythms

Figure 1

From: Wavelet analysis of circadian and ultradian behavioral rhythms

Figure 1

Periodogram analysis of a time series. (A) Simulated time series with 16 hours of period 5.3 h alternating with 8 hours of period 1.62 h, plus white noise. (B) Fourier, MESA, and Lomb-Scargle periodograms all have similar large spikes at harmonics 24/4=6 h and 24/5=4.8 h, plus small spikes at harmonics 24/7=3.43 h, 24/8=3 h, and 24/9=2.67 h. Note the absence in all 3 periodograms of significant power at the ultradian periods 5.3 h and 1.62 h, marked by small arrows along the horizontal axis. (C) Inverse DFT of the first 18 harmonics. While the periodograms do not provide a direct means of detecting the ultradian periods of interest, if the underlying ultradian pattern is sufficiently regular (as is the case in this example), then taking the inverse DFT of the circadian harmonics can reveal what that pattern is.

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