Analytic signal spectrograms with optimized time-frequency resolution
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
Further, the sample scripts provided in the examples folder require the funcality of
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.gzcd 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).