Ultradian Wavelet Band Power

Partitions the activity variance into dyadic period bands with an undecimated (MODWT) Haar wavelet transform, isolating ultradian bands such as the about-90-minute, about-4-hour, and about-8-hour rhythms (Percival and Walden 2000; Leise 2013). Reports the energy, power, and fraction of total variance in each band.

Usage

ultradian.bandpower(
  counts,
  timestamps,
  bands = list(`90min` = c(1, 2), `4h` = c(2, 6), `8h` = c(6, 12)),
  epoch_length = 60
)

Arguments

counts

Numeric activity vector (minute epochs recommended).

timestamps

POSIXct timestamps, one per value.

bands

Named list of c(low_hours, high_hours) period bands (default about 90 min, about 4 h, about 8 h).

epoch_length

Epoch length in seconds (default 60).

Value

An object of class actiRhythm_bandpower: a per-band table (energy, power, fraction) and the per-level wavelet variance. Never errors.

References

Percival DB, Walden AT (2000). Wavelet Methods for Time Series Analysis. Cambridge University Press. doi:10.1017/CBO9780511841040 .

Leise TL (2013). “Wavelet analysis of circadian and ultradian behavioral rhythms.” Journal of Circadian Rhythms, 11, 5. doi:10.1186/1740-3391-11-5 .

Examples

ts <- seq(as.POSIXct("2024-01-01", tz = "UTC"), by = 60, length.out = 2 * 1440)
th <- as.numeric(difftime(ts, ts[1], units = "hours"))
ultradian.bandpower(100 + 50 * sin(2 * pi * th / 4), ts)   # a 4-hour rhythm
#> Ultradian Wavelet Band Power
#> 
#>   band low_h high_h  power fraction
#>  90min     1      2  248.2    0.199
#>     4h     2      6 1173.8    0.939
#>     8h     6     12  435.8    0.349
#>