The Python package optfrog comprises tools for the calculation of spectrograms with optimized time and frequency resolution. Gabor's uncertainty principle prevents both from beeing optimal simultaneously for a given window function employed in the underlying short-time Fourier analysis.
Aim of optfrog is to provide a time-frequency representation of the input signal with marginals that represent the original intensities per unit time and frequency similarly well. A tunable paramter might be adjusted to emphasize time or frequency resolution.

The tools provided by the optfrog package require the functionality of

• numpy (>=1.8.0rc1)
• scipy (>=0.13.0b1)

Further, the sample scripts provided in the examples folder require the funcality of

• matplotlib (>=1.2.1)

for generating figures as the one shown below.

Get a local copy of the repository and install optfrog by running

python setup.py install

from the commandline. The installation requires pythons setuptools.

In case you downloaded the source distribution optfrog-1.0.0.tar.gz from the folder dist onto a Unix system with user rights only, run

tar -xvf optfrog-1.0.0.tar.gz
cd optfrog-1.0.0/
python setup.py install --user

from the commandline. This, however will only install the optfrog tools without the examples folder. So make sure to also fetch a local copy of the examples provided here.

optfrog also comes with several sample programs in the examples directory. For example, changing to the examples folder and running

python example_optFrog.py

will compute a time-frequency resolution optimized spectrogram for an input signal characterizing a short intense optical pulse after propagation in a nonlinear waveguide. The above example script will generate the below figure in subfolder FIGS.

The center part of the figure shows an optFrog spectrogram for an exemplary input signal. The intesity of the spectrogram is normalized to a maximum value of unity. The subfigure on top allows to compare the intensity per unit time of the normalized analytic signal for the input data (gray line) to the time marginal obtained from the spectrogram (black line). The subfigure on the right shows the intensity per unit frequency of the analytic signal (gray line) as well as the frequency marginal computed from the spectrogram (black line).

We further prepared an optFROG compute capsule on Code Ocean, allowing to directly run and modify an exemplary simulation without the need to locally install the software.

The optfrog software package is derived from our research software and is described in

O. Melchert, U. Morgner, B. Roth, and A. Demircan, "OptFROG — Analytic signal spectrograms with optimized time–frequency resolution", SoftwareX 10, 100275 (2019)

Further use-cases demonstrating parts of the functionality of optfrog as a tool for signal analysis in ultrashort pulse propagation can be found under

O. Melchert, U. Morgner, B. Roth, I. Babushkin, and A. Demircan, "Accurate propagation of ultrashort pulses in nonlinear waveguides using propagation models for the analytic signal," Proc. SPIE 10694, Computational Optics II, 106940M (2018)

and

O. Melchert, S. Willms, S. Bose, A. Yulin, B. Roth, F. Mitschke, U. Morgner, I. Babushkin, and A. Demircan, "Soliton Molecules with Two Frequencies", Phys. Rev. Lett. 123, 243905 (2019)

This project is licensed under the MIT License - see the LICENSE.md file for details.

This work received funding from the Deutsche Forschungsgemeinschaft (DFG) under Germany’s Excellence Strategy within the Cluster of Excellence PhoenixD (Photonics, Optics, and Engineering – Innovation Across Disciplines) (EXC 2122, projectID 390833453).