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Smoothness-priors detrending

Source: R/ecg-detrend.R
smoothnessPriorsDetrend.Rd

Removes slow trends from a uniformly sampled series (e.g. an interpolated RR tachogram) using the smoothness-priors method of Tarvainen et al. (2002). The trend estimate is \((I + \lambda^2 D_2^\top D_2)^{-1} z\) where \(D_2\) is the second-order difference operator, and the detrended (stationary) component is \(z_{stat} = (I - (I + \lambda^2 D_2^\top D_2)^{-1}) z\). Larger lambda lowers the cutoff frequency, removing more low-frequency content.

Usage

smoothnessPriorsDetrend(series, lambda = 500, fs = 4)

Arguments

series

Numeric vector, uniformly sampled.

lambda

Smoothing parameter (regularisation). Higher values remove slower trends (lower cutoff). Default 500.

fs

Sampling rate of series in Hz, used only to report the approximate half-power cutoff frequency. Default 4.

Value

The detrended series (numeric vector, near-zero mean), carrying attributes lambda and cutoff_hz (the approximate half-power cutoff of the implied high-pass filter).

References

Tarvainen, M.P., Ranta-aho, P.O. & Karjalainen, P.A. (2002). An advanced detrending method with application to HRV analysis. IEEE Transactions on Biomedical Engineering, 49(2), 172-175.

See also

ecgHRVfreq

Examples

t <- seq(0, 60, by = 0.25)
x <- 0.01 * t + sin(2 * pi * 0.25 * t)   # slow trend + HF oscillation
xd <- smoothnessPriorsDetrend(x, lambda = 500, fs = 4)
abs(mean(xd)) < 1e-6
#> [1] TRUE