Lomb-Scargle Periodogram

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)

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.

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)

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.

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)
#> Lomb-Scargle Periodogram
#> ------------------------
#> Peak period:    2.0000
#> Peak frequency: 0.5000
#> Peak power:     99.5000
#> FAP:            0.0000e+00
#> Significance:   1.0000
#> 
#> Frequency grid: 395 points (0.1000 to 9.9500)

# 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)