Figure 1
An artificially produced time series with an arbitrary maximum amplitude of one. It is a square wave with 20% white noise added. The power in the series is: 0.62.
Figure 2
This is the autocorrelation of the data depicted in Figure1. Note the height of the third peak, which is the RI and equals 0.697.
Figure 3
This is the so-called Whitaker-Robinson “periodogram”, which is not the same as the true periodogram ss of Schuster.
Figure 4
The Discrete Fourier Transform of the test time series. The period is calculated to be 22.4. Note in particular the paucity of spectral estimates in the crucial range between 20 and 30 hours. This would normally be corrected in more advanced Fourier Transform algorithms, but at a cost (see text).
Figure 5
This is the MESA spectrum with the coefficients upped to 32X. The period reported is 22.88, compared to the known input of 23.0. The tiny discrepancy is likely a result of the 20% added noise in the signal.
Figure 6
This is the original data set after being filtered twice with a Butterworth recursive digital filter. The second pass reverses the filter’s introduction of a four-hour phase delay owing to its recursive nature.