| Name |  GUM2DFT |
|---|---|
| Type | Python |
| Date | 24.09.2021 |
Background
The Fourier transform and its counterpart for discrete time signals, the 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 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.
The corresponding scientific publication is
S. Eichstädt and V. Wilkens "
GUM2DFT -- A software tool for uncertainty evaluation of transient signals in the frequency domain". Meas. Sci. Technol. 27(5), 055001, 2016
For questions and remarks please contact 
Sascha Eichstädt.
The methods from this software are also part of the larger Python package PyDynamic, which is hosted on GitHub: https://github.com/PTB-PSt1/PyDynamic .
Methods
| GUM_DFT | calculation of DFT(x) and the associated covariance matrix |
|---|---|
| GUM_iDFT | calculation of iDFT(F) and the associated covariance matrix |
| DFT2AmpPhase | calculation of amplitude and phase from F and the assoc. covariance matrix |
| AmpPhase2DFT | calculation of real and imag part from ampl and phase and the assoc. covariance matrix |
| Time2AmpPhase | calculation of amplitude and phase from x and the assoc covariance matrix |
| AmpPhase2Time | calculation of x from amplitude and phase and the assoc. covariance matrix |
| GUMdeconv | calculation of deconvolution X=Y/H with assoc. covariance matrix (DFT domain) |
A detailled example of using the software can be downloaded here:download
The corresponding IPython notebook and more examples are part of the software download.