Cross Calibration by FFT Equalization

Abstract

The classical calibration problem is primarily concerned with comparing an approximate measurement method with a very precise one. Frequently, both measurement methods are very noisy, so we cannot regard either method as giving the true value of the quantity being measured. Sometimes, it is desired to replace a destructive or slow measurement method, by a noninvasive, faster or less expensive one. The simplest solution is to cross calibrate one measurement method in terms of the other. The common practice is to use regression models, as cross calibration formulas. However, such models do not attempt to discriminate between the clutter and the true functional relationship between the cross calibrated measurement methods. A new approach is proposed, based on minimizing the sum of squares of the differences between the absolute values of the Fast Fourier Transform (FFT) series, derived from the readings of the cross calibrated measurement methods. The line taken is illustrated by cross calibration examples of simulated linear and nonlinear measurement systems, with various levels of additive noise, wherein the new method is compared to the classical regression techniques. It is shown, that the new method can discover better the true functional relationship between two measurement systems, which is occluded by the noise.