Detection of variable frequency signals using a fast chirp transform

TL;DR

The paper introduces a Fast Chirp Transform (FCT), a new method analogous to FFT, designed for detecting signals with variable frequency, simplifying the process especially in gravitational wave detection.

Contribution

The work presents the FCT, a novel formalism for variable frequency signal detection that reduces the complexity of traditional matched filtering techniques.

Findings

FCT provides a simple formalism for variable frequency detection.

FCT reduces the need for complex filter families.

Potential applications in gravitational wave detection.

Abstract

The detection of signals with varying frequency is important in many areas of physics and astrophysics. The current work was motivated by a desire to detect gravitational waves from the binary inspiral of neutron stars and black holes, a topic of significant interest for the new generation of interferometric gravitational wave detectors such as LIGO. However, this work has significant generality beyond gravitational wave signal detection. We define a Fast Chirp Transform (FCT) analogous to the Fast Fourier Transform (FFT). Use of the FCT provides a simple and powerful formalism for detection of signals with variable frequency just as Fourier transform techniques provide a formalism for the detection of signals of constant frequency. In particular, use of the FCT can alleviate the requirement of generating complicated families of filter functions typically required in the conventional matched filtering process. We briefly discuss the application of the FCT to several signal detection problems of current interest.