fdars (version 0.3.3)

lomb.scargle: Lomb-Scargle Periodogram

Description

Computes the Lomb-Scargle periodogram for period detection in unevenly-sampled data. The Lomb-Scargle method is designed for irregularly spaced observations and reduces to the standard periodogram for evenly-spaced data.

Usage

lomb.scargle(fdataobj, oversampling = 4, nyquist_factor = 1)

Value

A list of class "lomb_scargle_result" with components:

frequencies

Vector of evaluated frequencies

periods

Corresponding periods (1/frequency)

power

Normalized Lomb-Scargle power at each frequency

peak_period

Period with highest power

peak_frequency

Frequency with highest power

peak_power

Maximum power value

false_alarm_probability

False alarm probability at peak

significance

Significance level (1 - FAP)

Arguments

fdataobj

An fdata object. Can have regular or irregular sampling.

oversampling

Oversampling factor for the frequency grid. Higher values give finer frequency resolution. Default: 4.

nyquist_factor

Maximum frequency as a multiple of the pseudo-Nyquist frequency. Default: 1.

Details

The Lomb-Scargle periodogram is particularly useful when:

• Data has gaps or missing observations

• Sampling is not uniform (e.g., astronomical observations)

• Working with irregular functional data

The algorithm follows Scargle (1982) with significance estimation from Horne & Baliunas (1986). For each test frequency, it computes:

$$P(\omega) = \frac{1}{2\sigma^2} \left[ \frac{(\sum_j (y_j - \bar{y}) \cos\omega(t_j - \tau))^2}{\sum_j \cos^2\omega(t_j - \tau)} + \frac{(\sum_j (y_j - \bar{y}) \sin\omega(t_j - \tau))^2}{\sum_j \sin^2\omega(t_j - \tau)} \right]$$

where \(\tau\) is a phase shift chosen to make the sine and cosine terms orthogonal.

References

Scargle, J.D. (1982). Studies in astronomical time series analysis. II. Statistical aspects of spectral analysis of unevenly spaced data. The Astrophysical Journal, 263, 835-853.

Horne, J.H., & Baliunas, S.L. (1986). A prescription for period analysis of unevenly sampled time series. The Astrophysical Journal, 302, 757-763.

See Also

estimate.period, sazed

Examples

# Regular sampling
t <- seq(0, 10, length.out = 200)
X <- matrix(sin(2 * pi * t / 2), nrow = 1)
fd <- fdata(X, argvals = t)
result <- lomb.scargle(fd)
print(result)

# Irregular sampling (simulated)
set.seed(42)
t_irreg <- sort(runif(100, 0, 10))
X_irreg <- matrix(sin(2 * pi * t_irreg / 2), nrow = 1)
fd_irreg <- fdata(X_irreg, argvals = t_irreg)
result_irreg <- lomb.scargle(fd_irreg)