The definition of a periodogram of unequally spaced data was subsequently further modified and analyzed by Jeffrey D . Scargle of NASA Ames Research Center, who showed that with minor changes it could be made identical to Lomb's least-squares formula for fitting individual sinusoid frequencies.
32.
Craymer explains that the simultaneous or in-context method, as opposed to the independent or out-of-context version ( as well as the periodogram version due to Lomb ), cannot fit more components ( sines and cosines ) than there are data samples, and further that:
33.
In 1963, J . F . M . Barning of Mathematisch Centrum, Amsterdam, handled unequally spaced data by similar techniques, including both a periodogram analysis equivalent to what is now referred to the Lomb method, and least-squares fitting of selected frequencies of sinusoids determined from such periodograms, connected by a procedure that is now known as matching pursuit with post-backfitting or orthogonal matching pursuit.
34.
I warn you, however, that unlike the clear and brilliant words you occasionally find in my columns, the " Science " piece contains sentences like this : " To capture the neap ( cq )-spring cyclicity in the BCC records, we reconstructed the core time sequence with a singular spectrum analysis ( SSA ) algorithm ( 14 ) followed by computation of the periodogram ."
35.
If the desired result is a power spectrum and noise or randomness is present in the data, averaging the magnitude components of the multiple DFTs is a useful procedure to reduce the variance of the spectrum ( also called a periodogram in this context ); two examples of such techniques are the Welch method and the Bartlett method; the general subject of estimating the power spectrum of a noisy signal is called spectral estimation.
36.
The parameter "'N "'is known to Matlab and Octave users as NFFT . When a periodogram is used to examine the detailed characteristics of an FIR filter or window function, "'N "'is chosen to be several multiples of the non-zero duration of the x [ n ] sequence, which is called " zero-padding " ( see Sampling the DTFT ).
37.
I warn you, however, that unlike the clear and brilliant words you occasionally find in my columns, the " Science " piece contains sentences like this : " To capture the neap ( cq )-spring cyclicity in the BCC records, we reconstructed the core time sequence with a singular spectrum analysis ( SSA ) algorithm ( 14 ) followed by computation of the periodogram ( Discrete Fourier transformation ) ( DFT ) ."
38.
In the 1920s Yule wrote three influential papers on time series analysis, " On the time-correlation problem " ( 1921 ), a critique of the variate difference method, an investigation of a form of spurious correlation ( 1926 ) and " On a Method of Investigating Periodicities in Disturbed Series, with Special Reference to Wolfer's Sunspot Numbers " ( 1927 ), which used an autoregressive model to model the sunspot time series instead of the established periodogram method of Schuster.
39.
Scargle states that his paper " does not introduce a new detection technique, but instead studies the reliability and efficiency of detection with the most commonly used technique, the periodogram, in the case where the observation times are unevenly spaced, " and further points out in reference to least-squares fitting of sinusoids compared to periodogram analysis, that his paper " establishes, apparently for the first time, that ( with the proposed modifications ) these two methods are exactly equivalent ."
40.
Scargle states that his paper " does not introduce a new detection technique, but instead studies the reliability and efficiency of detection with the most commonly used technique, the periodogram, in the case where the observation times are unevenly spaced, " and further points out in reference to least-squares fitting of sinusoids compared to periodogram analysis, that his paper " establishes, apparently for the first time, that ( with the proposed modifications ) these two methods are exactly equivalent ."
