Numerical differentiation: local versus global methods

In this article, we present investigations on several techniques for numerical differentiation of data. Local techniques are confronted with global approaches and the differences are discussed in detail. Two basic quantities are used for characterization of results: The variance of the difference of the true derivative and its estimate, and the smoothness of the estimate. We apply the different techniques to numerically produced data and demonstrate the application to data from an aeroacoustic experiment. As a result, we find that global methods are generally preferable if a smooth process shall be considered. For rough estimates local methods are acceptable.