Rather than just taking dot products of the data with sine and cosine waveforms directly, Scargle modified the standard periodogram formula to first find a time delay ? such that this pair of sinusoids would be mutually orthogonal at sample times " t j ", and also adjusted for the potentially unequal powers of these two basis functions, to obtain a better estimate of the power at a frequency, which made his modified periodogram method exactly equivalent to Lomb's least-squares method.
42.
Rather than just taking dot products of the data with sine and cosine waveforms directly, Scargle modified the standard periodogram formula to first find a time delay ? such that this pair of sinusoids would be mutually orthogonal at sample times " t j ", and also adjusted for the potentially unequal powers of these two basis functions, to obtain a better estimate of the power at a frequency, which made his modified periodogram method exactly equivalent to Lomb's least-squares method.
43.
Petr Van?ek, a Canadian geodesist of the University of New Brunswick, also proposed the matching-pursuit approach, which he called " successive spectral analysis " and the result a " least-squares periodogram ", with equally and unequally spaced data, in 1969 . He generalized this method to account for systematic components beyond a simple mean, such as a " predicted linear ( quadratic, exponential, . . . ) secular trend of unknown magnitude ", and applied it to a variety of samples, in 1971.
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