Periodograms are computed by zero-extending the IMF modes from 111 to 1024 points, then taking a discrete Fourier transform. The plotted data is the magnitude squared of each DFT value, divided by 1024 and multiplied by 2 (to account for the conjugate-symmetric spectrum). Data is NOT windowed before zero-extending.

Here is the duplication using a log-frequency axis for the periodograms:

duplicated-1

Here is the duplication using a linear period axis (1/frequency):

duplicated-2

Here’s a late addition to the post. I graphed the C3 IMF mode versus sunspot number, just like Willis did in his post. Except I put them on top of each other and scaled the data to be visually similar in amplitude. Also, the IMF is actually the negative of C3 as it seems easier to visually compare that way.

C3-vs-SunspotNumber

I’m not sure if I agree with Willis’ conclusions completely. Yes, the phase between C3 and sunspot number does vary throughout, but there is a 1:1 correlation between extrema in the two curves — every sunspot cycle has a corresponding maxima in the inverted C3 curve.

On the other hand, the amplitudes do NOT track so it would appear that C3 depends on other things besides just sunspots.

I don’t know….it seems like by at least some stretch of the imagination this could be considered a solar signal but there’s clearly a lot more going on there too.

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You are aware, I hope, that zero-padding the time sequence does NOT increase frequency resolution!

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Bernie,

Thanks for pointing that out. Yes, I knew that but was perhaps a little careless in the wording. The problem I had is that the author claimed a 10.7 year cycle was in the periodogram result. But, with a 1-year sample interval and 111 points the DFT has no such frequency point. I don’t know how the author came up with 10.7 — perhaps by removing 4 points as a 107 point DFT would have a 10.7 year cycle in it. I tried that but the result did not match. Then I just “interpolated” the result to see what would happen and the result looks a lot like the author’s published graph.

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