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Dispersion-Compensated Algorithm
================================
*Dispersion-Compensated Algorithm for the Analysis for Electromagnetic Waveguides*
This package allows you to map dispersive waveguide data from the frequency-domain to distance-domain, and vice versa. The benefit of this approach, compared to a standard Fourier transform, is that this algorithm compensates for dispersion. Normally, dispersion causes signals in the time-domain to broaden as the propagate, making it difficult to isolate or supress adjacent signals. In the distance-domain, the signals remain sharp, even over long distances, allowing you to easily identify, isolate or suppress specific signals.
For more information, see:
- J. D. Garrett and C. E. Tong, ["A Dispersion-Compensated Algorithm for the Analysis of Electromagnetic Waveguides",](https://ieeexplore.ieee.org/document/9447194) *IEEE Signal Processing Letters*, vol. 28, pp. 1175-1179, Jun. 2021, doi: [10.1109/LSP.2021.3086695](https://doi.org/10.1109/LSP.2021.3086695).
Example: Simple Waveguide Section
---------------------------------
Transmission through a 10" long gold-plated WR-2.8 waveguide:
<p align="center">
<img src="https://raw.githubusercontent.com/garrettj403/DispersionTransform/main/examples/results/simple-waveguide-frequency.jpg" width="400">
</p>
Below, the time-domain response (calculated by an IFFT) is compared to the distance-domain response. Notice how much sharper the distance-domain response is.
<p align="center">
<img src="https://raw.githubusercontent.com/garrettj403/DispersionTransform/main/examples/results/simple-waveguide-time-vs-distance.jpg" width="600">
</p>
Example: Waveguide Cavity Resonator
-----------------------------------
This is a quick example showing the power of the dispersion-compensated algorithm. See [the included notebook](https://github.com/garrettj403/DispersionTransform/blob/main/examples/example-waveguide-cavity.ipynb) for more information.
For this example, we will start with the frequency-domain response of a simple waveguide cavity resonator, as shown below. This is a 1 inch long WR-2.8 cavity. Whenever the length of the cavity is an integer number of the guided wavelength divided by two, there is a peak in transmission.
<p align="center">
<img src="https://raw.githubusercontent.com/garrettj403/DispersionTransform/main/examples/results/cavity-freq-domain.jpg" width="600">
</p>
In the distance-domain, we can see a series of reflections corresponding to different signal paths within the resonator. The first peak is the signal passing straight through the resonator (distance = 1 inch), the second peak is the signal that undergoes ones internal back-and-forth reflection (distance = 3 inch), etc.
<p align="center">
<img src="https://raw.githubusercontent.com/garrettj403/DispersionTransform/main/examples/results/cavity-distance-domain.jpg" width="600">
</p>
In the distance-domain, we can easily isolate the first peak and then return to the frequency-domain. The isolated reflection provides a very close match to theory.
<p align="center">
<img src="https://raw.githubusercontent.com/garrettj403/DispersionTransform/main/examples/results/cavity-peak1.jpg" width="600">
</p>
Likewise, we can easily isolate the 6th peak and return to the frequency-domain. This is impossible in the time-domain because there is too much broadening and overlap between adjacent reflections.
<p align="center">
<img src="https://raw.githubusercontent.com/garrettj403/DispersionTransform/main/examples/results/cavity-peak6.jpg" width="600">
</p>
Note: This example is similar to the example presented by [Garrett & Tong 2021](https://ieeexplore.ieee.org/document/9447194), but it is slightly different (e.g., different dimensions, different iris parameters, etc.). Please see this paper for more information.
Citing This Repo
----------------
If you use this code, please cite the following paper:
@article{Garrett2021,
author = {John D. Garrett and
Edward Tong},
title = {{A Dispersion-Compensated Algorithm for the Analysis of Electromagnetic Waveguides}},
volume = {28},
pages = {1175--1179},
month = jun,
year = {2021},
journal = {IEEE Signal Processing Letters},
doi = {10.1109/LSP.2021.3086695},
url = {https://ieeexplore.ieee.org/document/9447194}
}
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