# A Time-Frequency Analysis of Chirps in Gravitational Wave Data

## Faculty Mentor Name

Cameron Williams

## Format Preference

Poster

## Abstract

Gravitational waves, first hypothesized as a result of Einstein’s general theory of relativity, were first measured by the Laser Interferometer Gravitational-Wave Observatory (LIGO). These gravitational waves measured from LIGO consist of black hole mergers and information of the inspiraling black holes can be determined such as their mass. The gravitational waves in this case are a specific example of chirps, which is a highly-oscillatory frequency within a signal. This project consists of branching off previous results of a generalization of the Fourier Transform to be able to construct a software library to analyze these waves and generalizing important results in signal processing such as the Shannon sampling theorem to create a strong mathematical foundation for analyzing chirp data, with a focus in extracting chirps from gravitational waves and filtering unwanted noise from the data.

A Time-Frequency Analysis of Chirps in Gravitational Wave Data

Gravitational waves, first hypothesized as a result of Einstein’s general theory of relativity, were first measured by the Laser Interferometer Gravitational-Wave Observatory (LIGO). These gravitational waves measured from LIGO consist of black hole mergers and information of the inspiraling black holes can be determined such as their mass. The gravitational waves in this case are a specific example of chirps, which is a highly-oscillatory frequency within a signal. This project consists of branching off previous results of a generalization of the Fourier Transform to be able to construct a software library to analyze these waves and generalizing important results in signal processing such as the Shannon sampling theorem to create a strong mathematical foundation for analyzing chirp data, with a focus in extracting chirps from gravitational waves and filtering unwanted noise from the data.