On the use of FFTs to pick out periods:
EXCEL has a maximum count of 4096 points
Other programmes will be different.
Taking EXCEL’s case and monthly time intervals will give you
a total of 341 years of data – just about 20 years less than the full CET
record Enough you may say to determine any 100 year or less cycles.
However these are the yearly data points above 50 years –
you will get no resolution better than these from EXCEL. 341.33 , 170.67, 113.78,
85.33, 68.27, 56.89, 48.76, 42.67
Really not very good above 50 years.
Here are a couple of plots showing the problem:
Note you loose te 65 and 80 year periods into one hump
Add a bit of separation and 2 peaks are produce but at periods of 57 and 85 years not 55 and 90 - you only get output at resolved points listed above.
Most people show their plots with wonderfully rounded curves:
This contains no data extra but the rounding makes it look as if there is more data than before.
Here's some indication of the extraction of data from a noisy signal - first the signal,
3 equal amplitude sine waves added
Next add in some noise
Next use EXCELs built in FFT
And the 3 sine waves become visible (Just) Note that the 90 year signal is much attenuated.
So what about using a different programme for the FFT. Using the same 4096 points from the EXCEL programme and inputting these to a SPICE analysis gives the following un-windowed plot (note the x axis is in 1/year)
Because all FFT generation is looking at a window of the data then any data that has a discontinuity at beginning and end will cause invalid FFTs. The spice programme has a number of available windowing functions to lessen this effect. The plot below shows the effect of a Hamming filter used on the data. Note that the level to the left has been much reduced. Also note that there is no extra data in these plots compared to the EXCEL plots Also note that the vertical scale is logarithmic EXCEL in the plots above is linear
So now try 1500year sequence of the same frequencies:
A lot more detail but still not good detail in the longer periods.
So just how people use records of less than 300 years and claim periods of 100 years. The data is not there, there is no way of increasing the resolution. If the data is not there then claiming long period "oscillations" are just incorrect and trying to equate periods of 50+ years to planetary motion is just "silly" - there is insufficient data!!.
