Smoothing and Differentiation of Data by Simplified Least Squares Procedures

Abstract

In attempting to analyze, on digital computers, data from basically continuous physical experiments, numerical methods of performing familiar operations must be developed. The operations of differentiation and filtering are especially important both as an end in themselves, and as a prelude to further treatment of the data. Numerical counterparts of analog devices that perform these operations, such as RC filters, are often considered. However, the method of least squares may be used without additional computational complexity and with considerable improvement in the information obtained. The least squares calculations may be carried out in the computer by convolution of the data points with properly chosen sets of integers. These sets of integers and their normalizing factors are described and their use is illustrated in spectroscopic applications. The computer programs required are relatively simple. Two examples are presented as subroutines in the FORTRAN language. © 1964, American Chemical Society. All rights reserved.