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CLEANest example from Grant Foster’s 1995 paper using VStar

Grant Foster’s 1995 CLEANest Fourier Spectrum paper (Foster, G., 1995, “The CLEANest Fourier Spectrum”, The Astronomical Journal, vol 109, no 4, 1889–1902­) gives a number of examples of applying the CLEANest algorithm to datasets, artificial and real. Two of these use AAVSO visual magnitude estimates: S Ori and AA Cas.

This post shows VStar’s CLEANest implementation applied to AA Cas. Foster 1995 uses an AA Cas dataset in the JD range 2447500 to 2449500. The following shows that dataset loaded from the AAVSO International Database (AID) via VStar’s file menu.

aa Cas Visual JD 2447500 to 2449500

A DCDFT with frequency range can be initiated from VStar’s Analysis menu, selecting the Visual band and specifying minimum and maximum frequencies, the range over which to scan, and frequency resolution over the range.

This results in the following power spectrum (in the Power vs Frequency pane) with the orange squares showing peaks or “top hits”.

aa Cas Visual JD 2447500 to 2449500 power spectrum

These top hits are shown in the next diagram in tabular form.

aa Cas Visual JD 2447500 to 2449500 selection for input to CLEANest(7)

In this example, seven top hits have been selected using combinations of shift-click and control-click  (Windows) or command-click (Mac). The initial input values to CLEANest are not stated in Foster 1995 (section 5, page 1900), but the rows selected above fairly closely correspond to what I think they should be.

Clicking the CLEANest button opens this dialog from the Top Hits pane.

aaCas CLEANest(7) input dialog

Clicking OK here adds seven new top hits with the same power value, shown multiply-selected in the top hits list and annotated on the power spectrum.

Now click Create Model in the Top Hits pane and the following dialog will open.

aaCas CLEANest(7) model creation dialog

Click OK and the main plot will have an additional “model” series added. Dismiss the main DCDFT dialog to return to the main VStar window.

aa Cas Visual JD 2447500 to 2449500 model from CLEANest(7)

Something on my TODO list is to make the model series continuous rather than discrete as it currently appears. The residuals for this model can be viewed by opening the Plot Control dialog from the View menu and setting it as shown, including changing the Days per Mean Series Bin (and clicking Apply).

Dismissing the dialog changes the plot to look like this.

aa Cas Residuals and binned means from Visual JD 2447500 to 2449500 CLEANest(7)

Performing a DCDFT on the residuals with the same frequency parameters as for the visual series, but by selecting the residuals gives the following power spectrum.

aa Cas power spectrum from Residuals

Looking at the Power axis suggests that there is very little discrimination between any of the frequencies.

In addition, the ANOVA value in the Info dialog (File menu) also suggests that there is unlikely to be any signal remaining to be found in the residuals, i.e. the null hypothesis that there is no significant signal present should be accepted.

aa Cas ANOVA from Residuals

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