Figure 1
This is a low interest informal article, I’ll chat, where it is easier to do as a new article than as a huge comment to an existing article.
I’ve been taking a close look at some of the TSI data to see what I can find. Other matters need my attention so I am wrapping up for the moment, more can be done later on.
I’m exclusively working with ACRIM3 daily data.
This has missing days. I decided to low pass filter the data at 0.2 year which has the effect of interpolating over the missing data and remove the intense high frequency noise which would make what I tended to do unnecessarily difficult. The removed content has a large solar rotation component but proper filtering will not lose any lower frequency information in the removed data.
In addition I decided to keep at daily data as a way of reducing objection to decimation, even though this puts severe stress on this computer handling large data.
I then set in motion a very long software run finding an approximation, probably one of the largest I have ever done, 47 terms. Runtime spread over a number of computer on days amounted to one or two days, it’s a slow process. (deliberately restricted to a single CPU/FPU core, used about 8M of memory, left running in the background). This has almost completed, stopped it early but can be restarted anytime.
Figure 1 shows the input data used, final approximation and the difference.
The approximation can be output as an interactive live model. This is a non-discrete Fourier Transform where the model is the inverse. There is no proof of correctness, is heuristics under the label, do you want a good answer or no answer at all?
Figure 2
Plotting spot points as lines proved too involved for a quick view so points will have to do. Some of these are so close spaced they seem to be one.
This result might seem illogical or wrong yet see figure 1. Phase is not being shown. Possibly most dramatic is the binning problem of discrete where the few available spot periods as a complex pair are all that exists, everything has to be lumped into what is available. Non discrete has no limitation but here I am relying on software discovering a good fit.
Figure 3
There are three traces on a restricted periodic range around the area of interest of the paper.
Identical software settings have been used to create each, providing the spectra of the input data used, the model (or approximation) which overlay, and the spectra of the remainder from subtracting the approximation from the data. Separation is about 10x (20dB).
What next?
For demonstration purposes lets do something very simple but suggestive of things perhaps useful.
Figure 4
I hope without causing too much contention, I’ve chosen the very close pair of periods and of almost identical amplitude. Here they are plotted together with their sum. Keep in mind there are no actual constant waves, all approximating. Validity is up to human judgement.
The two interfere, beating together with the effect of producing an amplitude modulated sum wave. Summation is the same as an inverse transform but many who think they understand transforms fail to recognise this form.
One critical thing to point out, very similar amplitude and period but the phase is very different. (I have exact numbers, not important here)
They go through cancellation.
Figure 5
Not perfect but good enough here, take the Hilbert transform of the sum(), providing the envelope, which is the amplitude of the wave.
What happens if we do wave / envelope point by point?
Figure 6
Also not perfect but useful, it has the effect of creating constant amplitude.
What is the period of the combination? I have software which can pretty accurately measure this and the phase based on a fragment of the above. If that had been a combination of more than two waves it is easiest to measure the result. Perhaps too it can be compared with other things.
I’ll leave it at that but comment on what next
The paper is suggesting the sun brightens up when facing certain outside bodies. We are viewing from earth. If this is correct there will be some kind of variable wave pattern in TSI.
I’ve created a very high resolution interactive model allowing what-if.
I think some candidate data should be created using ephemeris so that a compare can be done to see if anything matches.
Off to other things, don’t want to get deeply involved here.
Post by Tim Channon
[time of publication was about 2am 6th, has been slipped back to appear before previous post –Tim]
Tallbloke's Talkshop 
Very nice work Tim.
Am I correct in thinking the beat period is 105,06 years?
i.e. 1.03*1.02/(1.03-1.02)
Can you specify the ‘candidate data from ephemeris’ you would need?
For those two yes (the exact figures give about the same number) but ignore it because this analysis must be taken as local in time, zero predictability. If I extend the effect for several hundred years the penny would drop. As it happens if I add in a term at 0.51y which might be related the wave turns very different, eyebrow raising here. Don’t know what it means.
So hence choose something simple to illustrate how a bending effect can be removed to get out a number.
Doesn’t look terribly hard, choose a candidate planet and notionally figure how it is “illuminating” the sun and what the earth sees of this.
Need to do this at good enough resolution, no problem.
Once the math is worked out we can get various signals. Look and see if any make sense.
Matching signals is a strong method.
Venus is sometimes supposed to do things, however, as I recall it is earth which is the nearest active planet, magnetic effect. Since this is more or less the observation platform that might pose problems if it is doing things to the signals. Gravity, magnetic, wind, what?