What is recorded here?
Lomb analyzes sinusoidal least-squares spectra for unequally spaced observations, deriving fixed-frequency Gaussian-noise behavior and the correlation of spectral heights at different frequencies, with astronomical numerical illustrations. Astronomical observations often arrive at irregular times because daylight, weather and telescope access interrupt sampling. Fitting a sinusoid at each candidate frequency gives a meaningful least-squares measure of how much variation that frequency explains. Lomb studies how this measure behaves under random noise and why apparent peaks at different frequencies can be related. That makes the spectrum easier to interpret, but it does not make the largest peak a guaranteed true period. Searching many frequencies, estimating the mean or variance, and resolving sampling aliases require additional care.
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Scientific scope
The target is the 1976 Astrophysics and Space Science 39(2), pages 447-462 paper. The formulas are not an independently certified executable transcription. Fits sine/cosine coefficients at a given frequency with zero-mean observations, independent zero-mean equal-variance errors and a nonsingular two-column design. Fixed-frequency Gaussian-noise reduction is scaled chi-square with two degrees of freedom; subtracting a sample mean or estimating variance requires the corresponding covariance/distribution treatment. Numerical examples use an observed-variance approximation; normalized power is not automatically that same chi-square variable. Cross-frequency correlation and aliases remain; searched-maximum significance does not follow from independent fixed-frequency tests. Section 5 approximations and the reported 11 noise/10 signal simulations are not universal guarantees. A noise-free pattern match need not identify a unique period: integer-time aliases can coincide. Earlier Barning/Vanicek and later Scargle work remain distinct; no complete proof certification.
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- Lomb: statistical analysis of least-squares spectra for irregular observations; exact original technical journal scan
- Publisher-deposited exact1976 Lomb journal identity
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People and systems
N. R. Lomb
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English catalogue narrative
Lomb: statistical analysis of least-squares spectra for irregular observations
Lomb analyzes sinusoidal least-squares spectra for unequally spaced observations, deriving fixed-frequency Gaussian-noise behavior and the correlation of spectral heights at different frequencies, with astronomical numerical illustrations.
Astronomical observations often arrive at irregular times because daylight, weather and telescope access interrupt sampling. Fitting a sinusoid at each candidate frequency gives a meaningful least-squares measure of how much variation that frequency explains. Lomb studies how this measure behaves under random noise and why apparent peaks at different frequencies can be related. That makes the spectrum easier to interpret, but it does not make the largest peak a guaranteed true period. Searching many frequencies, estimating the mean or variance, and resolving sampling aliases require additional care.
Scientific scope
The target is the 1976 Astrophysics and Space Science 39(2), pages 447-462 paper. The formulas are not an independently certified executable transcription. Fits sine/cosine coefficients at a given frequency with zero-mean observations, independent zero-mean equal-variance errors and a nonsingular two-column design. Fixed-frequency Gaussian-noise reduction is scaled chi-square with two degrees of freedom; subtracting a sample mean or estimating variance requires the corresponding covariance/distribution treatment. Numerical examples use an observed-variance approximation; normalized power is not automatically that same chi-square variable. Cross-frequency correlation and aliases remain; searched-maximum significance does not follow from independent fixed-frequency tests. Section 5 approximations and the reported 11 noise/10 signal simulations are not universal guarantees. A noise-free pattern match need not identify a unique period: integer-time aliases can coincide. Earlier Barning/Vanicek and later Scargle work remain distinct; no complete proof certification.
People and systems
N. R. Lomb