Hilbert-Huang Instantaneous Phase and Frequency

Computes the instantaneous amplitude, phase, and period of a circadian intrinsic mode function via its analytic signal (Huang et al. 1998). Where the cosinor gives one acrophase for the whole recording, the instantaneous phase tracks the rhythm cycle by cycle, and the spread of the instantaneous period measures how stationary the circadian band is.

Usage

hilbert.huang(x, timestamps = NULL, imf = NULL, epoch_length = 60)

Arguments

x

A actiRhythm_emd object, or a numeric activity vector (then timestamps is required).

timestamps

POSIXct timestamps (required when x is numeric).

imf

Which IMF to analyse; default is the circadian IMF of the EMD object.

epoch_length

Epoch length in seconds (default 60; used when x is numeric).

Value

An object of class actiRhythm_hht: the instantaneous amplitude, phase, and period series, plus the mean instantaneous period and its SD, mean amplitude and its CV, and the fraction of time the period stays in 20-28 h. Never errors.

References

Huang NE, Shen Z, Long SR, Wu MC, Shih HH, Zheng Q, Yen NC, Tung CC, Liu HH (1998). “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis.” Proceedings of the Royal Society A, 454(1971), 903–995. doi:10.1098/rspa.1998.0193 .

See also

circadian.emd

Examples

ts <- seq(as.POSIXct("2024-01-01", tz = "UTC"), by = 600, length.out = 6 * 144)
th <- as.numeric(difftime(ts, ts[1], units = "hours"))
e <- circadian.emd(100 + 60 * cos(2 * pi * th / 24), ts, epoch_length = 600)
hilbert.huang(e)
#> Hilbert-Huang Instantaneous Dynamics
#> 
#>   Instantaneous period: 23.81 h (SD 3.59)
#>   Instantaneous amplitude: 56.3 (CV 0.28)
#>   Time in 20-28 h band: 92%
#>