A general method of computing the derivative of experimental data

Abstract

Many scientific and engineering investigations require the extraction of the first derivative from experimental data. Direct numerical differentiation is usually impractical because this amplifies the noise in the data, leading to unreliable results. This investigation shows that the problem of differentiating experimental data can be converted into one of solving an integral equation of the first kind. Tikhonov regularization is used to solve this integral equation, leading to a smooth first derivative. By using the built-in regularization parameter in the method noise amplification is kept under control. The performance of this method is demonstrated by applying it to data taken from the literature.