Optimal sample length for calculating transfer functions from discrete experimental data

Abstract

Transfer functions are useful tools in observing the behaviour of non-linear systems. Transfer functions convert an input signal into an output signal, and for non-linear systems can be calculated separately for each order of response using the Volterra series. The Volterra series quantifies the linear and non-linear responses separately for systems with either Gaussian or non-Gaussian inputs, and is particularly useful when calculating transfer functions from experimental data, as the calculations can be performed using a discrete frequency domain format. The application of the Volterra series to discrete experimental data requires careful consideration of various factors that impact on the successful calculation of transfer functions. The single largest problem faced when using discrete experimental data is the difficultly presented when determining the optimal sample length of the data adopted during the calculation process. Equal lengths of sample data are extracted from each individual record to calculate averaged input and output spectra. When using experimental data of finite record length, a trade off between the number of sample lengths obtained from each record and the frequency interval of the resulting transfer functions occurs. Here we explore those factors that lead to the selection of an optimal sample length. We begin with an overview of the Volterra series approach, and how experimental data can be used to calculate transfer functions. The factors that influence the selection of the optimal sample length are described and methods outlined that ensure the most meaningful results are obtained. We demonstrate these methods using the results from an experimental procedure performed on a model Tension Leg Platform.