Least-squares fitting a smooth curve to radiocarbon calibration data

We Fourier transformed and filtered calibration curve data to compensate for the averaging effect of radiocarbon-dating sets of adjacent tree rings. A Wiener Filter was also applied to minimize the effects of the counting errors of the dates on the resulting calibration curve and to produce a least-squares curve through the data. The method is illustrated using a short C-14-dated tree-ring sequence from New Zealand to produce a calibration curve at yearly intervals for New Zealand matai (Prumnopitys taxifolia). The resulting curve has a nominal standard error of 10 +/- 3 yr, which is ca. half the average standard error of the original raw data.