pytempscsp 1.0.5

Temporal Scale-Space Toolbox for Python.

pytempscsp : Temporal Scale Space Toolbox for Python

For performing temporal smoothing with the time-causal limit kernel and for computing discrete temporal derivative approximations by applying temporal difference operators to the smoothed data.

For examples of how to apply these functions for smoothing temporal signals to different temporal scales in a fully time-causal manner, please see the enclosed Jupyter notebook tempscspdemo.ipynb.

For more technical descriptions about the respective functions, please see the documentation strings for the respective functions in the source code in tempscsp.py.

The actual computations of the smoothed signals and the temporal derivatives is performed with computationally very efficient first-order recursive filters and small support temporal difference operators. For more explicit visualizations of the equivalent smoothing filters and temporal derivative computation filters, please see the enclosed Jupyter notebook kernelgraphs-ref.ipynb.

Time-causal temporal derivatives and bandpass wavelets

For examples of how to use extensions of this code for computing time-causal temporal derivatives, please see the enclosed Jupyter notebooks sineexpwave.ipynb, vibration.ipynb and cymbal44.ipynb.

For examples of how to use extensions of this code for computing bandpass wavelets based on either (i) differences-of-time-causal-limit-kernels (DoT), (ii) differences-of-Gaussians (DoG) or (iii) differences-of-exponentials (DoE), please see the enclosed Jupyter notebooks bandpass-blocks.ipynb and bandpass-riemann.ipynb.

For more technical descriptions about the respective functions, please see the documentation strings for the respective functions in the source code in tempscsel.py and bandpass.py.

Dependencies

Some parts of the code depend on the pyscsp library available at https://github.com/tonylindeberg/pyscsp.

The Jupyter notebooks for computing visualizations of bandpass wavelets depend on a function in the PyWavelets library for generating the input data.

Installation

This package is available through pip and can installed by

pip install pytempscsp

This package can also be downloaded directly from GitHub:

git clone [e-mail]:tonylindeberg/pytempscsp.git

References

Lindeberg (2023) "A time-causal and time-recursive temporal scale-space representation of temporal signals and past time", Biological Cybernetics 117 (1-2): 21-59. (Open Access)

Lindeberg (2026) "Time-causal and time-recursive wavelets", Frontiers in Signal Processing, to appear, preprint at arXiv:2510.05834. (Open Access)

Lindeberg (2016) "Time-causal and time-recursive spatio-temporal receptive fields", Journal of Mathematical Imaging and Vision 55(1): 50-88. (Open Access)

The time-causal limit kernel was first defined in Lindeberg (2016), however, then also in combination with a spatial domain, and experimentally tested on video data. The later overview paper (Lindeberg 2023) gives a dedicated treatment for a purely temporal domain, and also with relations to Koenderink's scale-time kernels and the ex-Gaussian kernel.

The extension to time-causal temporal derivatives was first performed in Lindeberg (2016), additionally considered in Lindeberg (2023) and then extended to bandpass wavelets and more general time-causal wavelets in Lindeberg (2026).