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

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.

13 pages, 1 table, 16 figures; scheduled for publication on Phys. Rev. D 62

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• Optimum Placement of Post-1PN GW Chirp Templates Made Simple at any Match Level via Tanaka-Tagoshi Coordinates
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