Redshift determination through weighted phase correlation: a linearithmic implementation

TL;DR

This paper introduces a fast, stable algorithm for redshift determination in quasars using weighted phase correlation, achieving comparable accuracy to existing methods but with improved computational efficiency.

Contribution

The paper presents a novel linearithmic algorithm for redshift determination that is faster and more numerically stable than previous quadratic-time methods.

Findings

Achieves O(N log N) computational complexity.

Provides redshift uncertainties and confidence measures.

Performance comparable to SDSS pipeline.

Abstract

We present a new algorithm having a time complexity of O(N log N) and designed to retrieve the phase at which an input signal and a set of not necessarily orthogonal templates match best in a weighted chi-squared sense. The proposed implementation is based on an orthogonalization algorithm and thus also benefits from high numerical stability. We apply this method successfully to the redshift determination of quasars from the twelfth Sloan Digital Sky Survey (SDSS) quasar catalogue and derive the proper spectral reduction and redshift selection methods. Derivations of the redshift uncertainty and the associated confidence are also provided. The results of this application are comparable to the performance of the SDSS pipeline, while not having a quadratic time dependence.