# A New Approach for Measuring Power Spectra and Reconstructing Time Series in Active Galactic Nuclei

## TL;DR

This paper introduces a Bayesian-based method leveraging Fourier transforms to accurately measure power spectra and reconstruct time series in active galactic nuclei, improving analysis efficiency and model comparison.

## Contribution

It presents a novel approach that models AGN stochastic variations in the frequency domain using Gaussian random variables, enabling improved spectral analysis and reconstruction.

## Key findings

- Effective power spectrum measurement in AGNs
- Enhanced time series reconstruction accuracy
- Facilitated model comparison using Bayesian framework

## Abstract

We provide a new approach to measure power spectra and reconstruct time series in active galactic nuclei (AGNs) based on the fact that the Fourier transform of AGN stochastic variations is a series of complex Gaussian random variables. The approach parameterizes a stochastic series in frequency domain and transforms it back to time domain to fit the observed data. The parameters and their uncertainties are derived in a Bayesian framework, which also allows us to compare the relative merits of different power spectral density models. The well-developed fast Fourier transform algorithm together with parallel computation enable an acceptable time complexity for the approach.