# Least-squares Spectral Analysis

Least-squares Spectral Analysis

Least-squares spectral analysis (LSSA) is a method of estimating a frequency spectrum, based on a least squares fit of sinusoids to data samples, similar to Fourier analysis. Fourier analysis, the most used spectral method in science, generally boosts long-periodic noise in long gapped records; LSSA mitigates such problems.

LSSA is also known as the Vaníček method after Petr Vaníček, and as the Lomb method (or the Lomb periodogram) and the Lomb–Scargle method (or Lomb–Scargle periodogram), based on the contributions of Nicholas R. Lomb and, independently, Jeffrey D. Scargle. Closely related methods have been developed by Michael Korenberg and by Scott Chen and David Donoho.

Read more about Least-squares Spectral Analysis:  Historical Background, The Vaníček Method, The Lomb–Scargle Periodogram, Korenberg's "fast Orthogonal Search" Method, Chen and Donoho's "basis Pursuit" Method, Palmer's Chi-squared Method, Applications, Implementation

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Least-squares Spectral Analysis - Implementation
... whereas Vaníček's original method does a full simultaneous least-squares fit by solving a matrix equation, partitioning the total data variance between the specified sinusoid ... Such a matrix least-squares solution is natively available in MATLAB as the backslash operator ... Craymer explains that the least-squares method, as opposed to the independent or periodogram version due to Lomb, can not fit more components (sines and cosines) than there are data samples, and ...

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