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Mathematical Modelling and Data Analysis

Department 8.4

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Title: GUM2DFT — a software tool for uncertainty evaluation of transient signals in the frequency domain
Author(s): S. Eichstädt and V. Wilkens
Journal: Measurement Science and Technology
Year: 2016
Volume: 27
Issue: 5
Pages: 055001
DOI: 10.1088/0957-0233/27/5/055001
Keywords: dynamic measurements; deconvolution; discrete Fourier transform; uncertainty;
Tags: 8.42, Dynamik
Abstract: The Fourier transform and its counterpart for discrete time signals, the discrete Fourier transform (DFT), are common tools in measurement science and application. Although almost every scientific software package offers ready-to-use implementations of the DFT, the propagation of uncertainties in line with the guide to the expression of uncertainty in measurement (GUM) is typically neglected. This is of particular importance in dynamic metrology, when input estimation is carried out by deconvolution in the frequency domain. To this end, we present the new open-source software tool GUM2DFT , which utilizes closed formulas for the efficient propagation of uncertainties for the application of the DFT, inverse DFT and input estimation in the frequency domain. It handles different frequency domain representations, accounts for autocorrelation and takes advantage of the symmetry inherent in the DFT result for real-valued time domain signals. All tools are presented in terms of examples which form part of the software package. GUM2DFT will foster GUM-compliant evaluation of uncertainty in a DFT-based analysis and enable metrologists to include uncertainty evaluations in their routine work.

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