摘要： In the present paper, a new criterion is derived to obtain the optimum fitting curve while using Cubic B-spline basis functions to remove the statistical noise in the spectroscopic data. In this criterion, firstly, smoothed fitting curves using Cubic B-spline basis functions are selected with the increasing knot number. Then, the best fitting curves are selected according to the value of the minimum residual sum of squares (RSS) of two adjacent fitting curves. In the case of more than one best fitting curves, the authors use Reinsch’s first condition to find a better one. The minimum residual sum of squares (RSS) of fitting curve with noisy data is not recommended as the criterion to determine the best fitting curve, because this value decreases to zero as the number of selected channels increases and the minimum value gives no smoothing effect. Compared with Reinsch’s method, the derived criterion is simple and enables the smoothing conditions to be determined automatically without any initial input parameter. With the derived criterion, the satisfactory result was obtained for the experimental spectroscopic data to remove the statistical noise using Cubic B-spline basis functions.
关键词：Spectroscopic data;Automatic smoothing;Spline function
Abstract：In the present paper, a new criterion is derived to obtain the optimum fitting curve while using Cubic B-spline basis functions to remove the statistical noise in the spectroscopic data. In this criterion, firstly, smoothed fitting curves using Cubic B-spline basis functions are selected with the increasing knot number. Then, the best fitting curves are selected according to the value of the minimum residual sum of squares (RSS) of two adjacent fitting curves. In the case of more than one best fitting curves, the authors use Reinsch’s first condition to find a better one. The minimum residual sum of squares (RSS) of fitting curve with noisy data is not recommended as the criterion to determine the best fitting curve, because this value decreases to zero as the number of selected channels increases and the minimum value gives no smoothing effect. Compared with Reinsch’s method, the derived criterion is simple and enables the smoothing conditions to be determined automatically without any initial input parameter. With the derived criterion, the satisfactory result was obtained for the experimental spectroscopic data to remove the statistical noise using Cubic B-spline basis functions.
Key words：Spectroscopic data;Automatic smoothing;Spline function
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