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Download "Band Pass by Fourier Methods", by G. Calderwood.

"Tuning in" to the Walnut

Tuned walnutTansfer function
Walnut spectrum

tuned circuitThe chart at the top left depicts a "tuned", or filtered, version of the λ variation of the Romanian Walnut bud, Bud1a, as it had manifested until 24th January, 2007.

Fourier Analysis of the λ variation of the Walnut bud produces the spectrum shown on the left. Superimposed in green on this spectrum is the similarly-produced spectrum of  the alignment of the Moon with Saturn.  The latter shows many peaks,  but the highest of them is the important one.  It is the "dominant", representing the period, or frequency, holding most of the "energy" of variation.  Not very surprisingly, it is close to the mean Inter-Alignment Period (mIAP) for the time span of this particular series.  It will be seen that there is a significant peak of λ "energy" co-inciding almost exactly with the Moon/Saturn dominant.

We might therefore expect to see variation in the actual λ chart corresponding to it. We would expect peaks or dips at the same intervals as the Saturn/Moon alignments.  And,  were it not for the many other spectral peaks, we would indeed see them. But there is a lot going on with the shape of this bud.  Other rhythms are present, besides the one in which we are interested, that obscure them. 

A spectrum is in effect just the list of simple, sinusoidal components which sum to the original data, presented as a graph.  The process of compiling the list is called Fourier Analysis.  The process of actually summing the components is called Fourier Synthesis.  If we have the list, then we can often isolate the spectral peaks that contain the components of most interest, simply by omitting from the synthesis those components of the spectrum that do not belong to those peaks.  But for all sorts of reasons it is not good to chop up the spectrum abruptly.  The discontinuities introduce falsifying spuriae into the synthesis.  It is better to run unwanted portions to zero gently, without discontinuity.

Here we have used a tuned filter to accomplish this.  It is a computer analogue of the electrical circuit shown above right, and makes use of resonance.  Its response can be tailored to make it more or less selective over a definable range of frequencies. The actual transfer function used on the Walnut spectrum is shown above the circuit.  This filter was tuned precisely to the  dominant of Moon/Saturn, made moderately selective, and applied to the Walnut's λ spectrum.

The synthesis of its output is the chart at the top left.

It is at once obvious from it that there is a λ rhythm in the Walnut corresponding well to the Moon/Saturn rhythm.  Indeed the peaks of it broadly co-incide in time with the actual Saturn alignments - though the troughs do not.  They tend to come about 8 to 9 days in advance of the Saturn alignments (that is, they have a phase shift of perhaps -9 days). Whichever of these - peak or trough - turns out to be the properly significant event for this bud, the general rhythm seems to be settling on Saturn, which we therefore provisionally take to be this bud's acknowledged planet.  Time and more data will say whether or not this is justified.

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Download "Band Pass by Fourier Methods", by G. Calderwood (zipped "Word" document).