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A software package for the analysis of dynamic measurements

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Python package for the analysis of dynamic measurements

The goal of this package is to provide a starting point for users in metrology and related areas who deal with time-dependent, i.e. dynamic, measurements. The initial version of this software was developed as part of a joint research project of the national metrology institutes from Germany and the UK, i.e. Physikalisch-Technische Bundesanstalt and the National Physical Laboratory.

Further development and explicit use of PyDynamic is part of the European research project EMPIR 17IND12 Met4FoF and the German research project FAMOUS.

PyDynamic offers propagation of uncertainties for

  • application of the discrete Fourier transform and its inverse
  • filtering with an FIR or IIR filter with uncertain coefficients
  • design of a FIR filter as the inverse of a frequency response with uncertain coefficients
  • design on an IIR filter as the inverse of a frequency response with uncertain coefficients
  • deconvolution in the frequency domain by division
  • multiplication in the frequency domain
  • transformation from amplitude and phase to a representation by real and imaginary parts

For the validation of the propagation of uncertainties, the Monte-Carlo method can be applied using a memory-efficient implementation of Monte-Carlo for digital filtering

The documentation for PyDynamic can be found on ReadTheDocs


If you just want to use the software, the easiest way is to run from your system's command line

pip install PyDynamic

This will download the latest version from the Python package repository and copy it into your local folder of third-party libraries. Note that PyDynamic runs with Python version 3.4 to 3.7. Usage in any Python environment on your computer is then possible by

import PyDynamic

or, for example, for the module containing the Fourier domain uncertainty methods:

from PyDynamic.uncertainty import propagate_DFT

Updates can then be installed via

pip install --upgrade PyDynamic

For collaboration we recommend forking the repository as described here , apply the changes and open a Pull Request on GitHub as described here . In this way any changes to PyDynamic can be applied very easily.

If you have downloaded this software, we would be very thankful for letting us know. You may, for instance, drop an email to one of the authors (e.g. Sascha Eichstädt, Björn Ludwig or Maximilian Gruber )


Uncertainty propagation for the application of a FIR filter with coefficients b with which an uncertainty ub is associated. The filter input signal is x with known noise standard deviation sigma. The filter output signal is y with associated uncertainty uy.

from PyDynamic.uncertainty.propagate_filter import FIRuncFilter
y, uy = FIRuncFilter(x, sigma, b, ub)    

Uncertainty propagation through the application of the discrete Fourier transform (DFT). The time domain signal is x with associated squared uncertainty ux. The result of the DFT is the vector X of real and imaginary parts of the DFT applied to x and the associated uncertainty UX.

from PyDynamic.uncertainty.propagate_DFT import GUM_DFT
X, UX = GUM_DFT(x, ux)

Sequential application of the Monte Carlo method for uncertainty propagation for the case of filtering a time domain signal x with an IIR filter b,a with uncertainty associated with the filter coefficients Uab and signal noise standard deviation sigma. The filter output is the signal *y and the Monte Carlo method calculates point-wise uncertainties uy and coverage intervals Py corresponding to the specified percentiles.

from PyDynamic.uncertainty.propagate_MonteCarlo import SMC
y, uy, Py = SMC(x, sigma, b, a, Uab, runs=1000, Perc=[0.025,0.975])

PyDynamic Workflow Deconvolution


  1. Implementation of robust measurement (sensor) models
  2. Extension to more complex noise and uncertainty models


If you publish results obtained with the help of PyDynamic, please cite

Sascha Eichstädt, Clemens Elster, Ian M. Smith, and Trevor J. Esward Evaluation of dynamic measurement uncertainty – an open-source software package to bridge theory and practice J. Sens. Sens. Syst., 6, 97-105, 2017, DOI: 10.5194/jsss-6-97-2017


Part of this work is developed as part of the Joint Research Project 17IND12 Met4FoF of the European Metrology Programme for Innovation and Research (EMPIR).

This work was part of the Joint Support for Impact project 14SIP08 of the European Metrology Programme for Innovation and Research (EMPIR). The EMPIR is jointly funded by the EMPIR participating countries within EURAMET and the European Union.


This software is developed at Physikalisch-Technische Bundesanstalt (PTB). The software is made available "as is" free of cost. PTB assumes no responsibility whatsoever for its use by other parties, and makes no guarantees, expressed or implied, about its quality, reliability, safety, suitability or any other characteristic. In no event will PTB be liable for any direct, indirect or consequential damage arising in connection with the use of this software.


PyDynamic is distributed under the LGPLv3 license with the exception of the module in the package misc, which is distributed under the GPLv3 license.

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