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A software package for the analysis of dynamic measurements

Project description


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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
  • 1-dimensional interpolation

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

Package diagram

The fundamental structure of PyDynamic is shown in the following figure.

PyDynamic package diagram

However, imports should generally be possible without explicitly naming all packages and modules in the path, so that for example the following import statements are all equivalent.

from PyDynamic.uncertainty.interpolate import make_equidistant
from PyDynamic.uncertainty import make_equidistant
from PyDynamic import make_equidistant


There is a quick way to get started but we advise to setup a virtual environment and guide through the process in the section Proper Python setup with virtual environment

Quick setup (not recommended)

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

pip install --user 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 versions 3.6 to 3.8. 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

Updating to the newest version

Updates can then be installed via

pip install --user --upgrade PyDynamic

Proper Python setup with virtual environment (recommended)

The setup described above allows the quick and easy use of PyDynamic, but it also has its downsides. When working with Python we should rather always work in so-called virtual environments, in which our project specific dependencies are satisfied without polluting or breaking other projects' dependencies and to avoid breaking all our dependencies in case of an update of our Python distribution.

If you are not familiar with Python virtual environments you can get the motivation and an insight into the mechanism in the official docs.

Create a virtual environment and install requirements

Creating a virtual environment with Python built-in tools is easy and explained in more detail in the official docs of Python itself.

It boils down to creating an environment anywhere on your computer, then activate it and finally install PyDynamic and its dependencies.

venv creation and installation in Windows

In your Windows command prompt execute the following:

> py -3 -m venv LOCAL\PATH\TO\ENVS\PyDynamic_venv
> LOCAL\PATH\TO\ENVS\PyDynamic_venv\Scripts\activate.bat
(PyDynamic_venv) > pip install PyDynamic
venv creation and installation on Mac and Linux

In your terminal execute the following:

$ python3 -m venv /LOCAL/PATH/TO/ENVS/PyDynamic_venv
$  /LOCAL/PATH/TO/ENVS/PyDynamic_venv/bin/activate
(PyDynamic_venv) $ pip install PyDynamic

Updating to the newest version

Updates can then be installed on all platforms after activating the virtual environment via:

(PyDynamic_venv) $ pip install --upgrade PyDynamic

Optional Jupyter Notebook dependencies

If you are familiar with Jupyter Notebooks, you find some examples in the examples and the tutorials subfolders of the source code repository. To execute these you need additional dependencies which you get by appending [examples] to PyDynamic in all of the above, e.g.

(PyDynamic_venv) $ pip install PyDynamic[examples]

Install known to work dependencies' versions

In case errors arise within PyDynamic, the first thing you can try is installing the known to work configuration of dependencies against which we run our test suite. This you can easily achieve with our version specific requirements files. First you need to install our dependency management package pip-tools, then find the Python version you are using with PyDynamic and finally install the provided dependency versions for your specific Python version. This is all done with the following sequence of commands after activating. Change the suffix -py38 according to the Python version you find after executing (PyDynamic_venv) $ python --version:

(PyDynamic_venv) $ pip install --upgrade pip-tools
Collecting pip-tools
Successfully installed pip-tools-5.2.1
(PyDynamic_venv) $ python --version
Python 3.8.3
(PyDynamic_venv) $ pip-sync requirements/dev-requirements-py38.txt requirements/requirements-py38.txt
Collecting [...]
Successfully installed [...]
(PyDynamic_venv) $

Contributing to PyDynamic

If you want to contribute code to the project you find additional set up and related information in our Contribution advices and tips.

If you have a feature request please take a look at the roadmap and the links provided there to find out more about planned and ongoing developments. If you have the feeling, something is missing, let us know by opening an issue.

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 )


We have collected extended material for an easier introduction to PyDynamic in the two subfolders examples and tutorials. In various Jupyter Notebooks and scripts we demonstrate the use of the provided methods to aid the first steps in PyDynamic. New features are introduced with an example from the beginning if feasible. We are currently moving this supporting collection to an external repository on GitHub. They will be available at in the near future.

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
  3. Introducing uncertainty propagation for Kalman filters

For a comprehensive overview of current development activities and upcoming tasks, take a look at the project board, issues and pull requests.


If you publish results obtained with the help of PyDynamic, please use the above linked Zenodo DOI for the code itself or 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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