Just like an integrator or low pass filter in Electronics the averaging mechanism distorts the signal present in the data. Averaging will produce both a reduction in amplitude and a phase shift for a sinusoidal signal. To determine the dampening factor for 20-year averaging I generated a number of sine waves of unit amplitude for a number of frequencies and subjected them to 20-year averaging. The resulting curve obtained by taking half the peak-to-peak amplitude is similar to what one would get for a low-pass filter. Lower frequencies corresponds to longer periods. T is the period in years.
The period for the three harmonic fit was T = 123.054 Julian years. The damping factors, D, were 0.957, 0.835 and 0.652 for the 1st, 2nd and 3rd harmonics respectively. Increasing the amplitude of the harmonics by dividing the corresponding damping factors produced small increases to the deviation from a straight line in the direction of the center of the data.
It may be difficult to find higher order harmonics in the data since they are more strongly damped and may be masked by the "noise."
No comments:
Post a Comment