MEASUREMENT ERROR ON DIGITALLY RECORDED SPECTRA

Abstract

Assuming the noise at each recorded data point is random and Gaussian, the measurement error of the Line position of a spectral line is shown Co be equal to \[ \frac{1}{\sqrt{2}} \cdot (ration\;of\;noise\;to\;signal)\cdot(FWHH)^{\frac{1}{2}} \] if the line positions are determined by the Local minima of the following, expression: \[ C(I) = \left|\begin{array}{llllll} I-1 & &I& +& M\\ \Sigma & (S(i) + N(i)) - &\Sigma& &&(S(i) + N(i))\\ i = I - M & &i& =& I + 1 \end{array}\right| \] where S(i) is the assumed noise-free signal at data point i N(i) is the noise at: data point i and M is a chosen integer. Both the measurement error and FWHH are defined by the unit of data point.