Problems of Smoothing and Differentiation of Data by Least-Squares Procedures and Possible Solutions

Smoothing and differentiation of experimental data sometimes necessitate least-squares polynomial fitting of a large number of data points at a time (17, 19, or 21 points) rather than 3, 5, or 7 points with repetition of the procedure for several Iterations. For a 5- or 7-polnt fit, one loses smoothing of only 2 or 3 points, respectively, at each end, and for a 19- or 21-polnt fit one loses 9 or 10 points, respectively, at each end. No other smoothing procedure is known today to handle the edge point smoothing and differentiation. In this paper a procedure is suggested for smoothing and differentiating essentially every data point. In addition, different orders of polynomial fits have been tried for the same data set. It is noticed that the parabolic fit gives the best smoothing of the noisy data set.