A Nearly Minimum Redundant Correlator Interpolation Formula for Gravitational Wave Chirp Detection

TL;DR

This paper derives a lower bound on the number of templates for gravitational wave chirp detection and introduces an efficient interpolation formula, improving computational efficiency while maintaining detection accuracy.

Contribution

It presents a nearly-minimum redundant correlator interpolation formula and extends the theory to post-Newtonian models, advancing gravitational wave detection methods.

Findings

Derived an absolute lower bound on template count for detection accuracy.

Introduced an explicit nearly-minimum redundant interpolation formula.

Compared computational and statistical properties with existing correlator methods.

Abstract

An absolute lower bound on the number of templates needed to keep the fitting factor above a prescribed minimal value $\Gamma$ in correlator bank detection of (newtonian) gravitational wave chirps from unknown inspiraling compact binary sources is derived, resorting to the theory of quasi-bandlimited functions in the $L^\infty$ norm. An explicit nearly-minimum redundant cardinal-interpolation formula for the (reduced, noncoherent) correlator is introduced. Its computational burden and statistical properties are compared to those of the plain lattice of (reduced, noncoherent) correlators, for the same $\Gamma$. Extension to post-newtonian models is outlined.