Dispersion-compensated algorithm for electromagnetic waveguides

# 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.

## Getting Started

You can install the CZT package using pip:

# to install the latest release (from PyPI)
pip install czt

# to install the latest commit (from GitHub)
git clone https://github.com/garrettj403/CZT.git
cd CZT
pip install -e .

# to install dependencies for examples
pip install -e .[examples]


## Example: Simple Waveguide Section

Transmission through a 10" long gold-plated WR-2.8 waveguide:

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.

## Example: Waveguide Cavity Resonator

This is a quick example showing the power of the dispersion-compensated algorithm. See the included notebook 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.

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.

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.

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.

Note: This example is similar to the example presented by Garrett & Tong 2021, 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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