EMRI_FrequencyDomainWaveforms

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EMRI_FrequencyDomainWaveforms

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# EMRI Frequency Domain Waveforms

This folder contains the scripts to reproduce the Frequency Domain EMRI Waveform analysis presented in [Fast and Fourier: Extreme Mass Ratio Inspiral Waveforms in the Frequency Domain](https://arxiv.org/abs/2307.12585). In `Tutorial_FrequencyDomain_Waveforms.ipynb` you can find how to generate the Frequency Domain (FD) waveforms and compare them to the Time Domain (TD) ones as in the following figure:

![time domain VS frequency domain](https://github.com/lorenzsp/EMRI_FourierDomainWaveforms/blob/main/figures/FD_TD_frequency.png)

The Frequency Domain implementation is now part of the package Fast EMRI Waveforms ([arxiv.org/2104.04582](https://arxiv.org/abs/2104.04582), [arxiv.org/2008.06071](https://arxiv.org/abs/2008.06071)). To run the scripts contained in this folder it is necessary to install the Fast EMRI Waveforms package available [here](https://github.com/BlackHolePerturbationToolkit/FastEMRIWaveforms/). You also need to install the codes in: `LISAanalysistools` and `Eryn` by running `python setup.py install` inside each folder.

The analysis presented in [Fast and Fourier: Extreme Mass Ratio Inspiral Waveforms in the Frequency Domain](https://arxiv.org/abs/2307.12585) can be reproduced using the scripts:
- emri_pe.py: runs an MCMC analysis of an EMRI source. Usage: 
    ```
    python emri_pe.py -Tobs 2.0 -M 1e6 -mu 10.0 -p0 12.0 -e0 0.35 -dev 7 -eps 1e-2 -dt 10.0 -injectFD 1 -template fd -nwalkers 16 -ntemps 1 -downsample 100
    ```
- check_mode_by_mode.py: scans the EMRI parameter space and compares the accuracy and performance of the time and frequency domain models. Usage: 
    ```
    python check_mode_by_mode.py -Tobs 1.0 -dev 5 -eps 1e-2 -dt 10.0 -fixed_insp 1 -nsteps 10
    ```
- Tutorial_FrequencyDomain_Waveforms.ipynb: describes the usage of the frequency domain waveform and compares it with the time domain
- Tutorial_FD_construction_single_mode.ipynb: describes the construction of the frequency domain waveform for a single harmonic

## Authors

* **Lorenzo Speri**
* Michael Katz
* Alvin J. K. Chua
* Scott A. Hughes
* Niels Warburton
* Jonathan E. Thompson
* Christian E. A. Chapman-Bird
* Jonathan R. Gair

EMRI_FrequencyDomainWaveforms

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