MG11 
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BINARY INSPIRAL CORRELATOR INTERPOLATION FORMULAS: CARDINAL vs. CHEBYSHEV

Two main philosophies have been hitherto suggested for reducing the computational cost of template-bank based maximum-likelihood detection (and source-prameter estimation) of gravitational waves from the inspiral phase of coalescing binary sources. In [1] and [2], capitalizing on the quasi-bandlimited property of the match function [3] and on Kotel’nikov theorem [4] for (quasi) band-limited stochastic processes, cardinal interpolation was proposed and evaluated. In [5], a different approach based on a quasi-minimax Chebyshev polynomial was proposed and tested. The mathematical structure, performance, and computational cost of these two alternative philosophies are discussed. The best performance of the Chebyshev approximant (in terms of smallest polynomial order required to guarantee a prescribed minimal-match) is obtained after mapping the chirp-time search interval into (-1,1) in such a way that the roots of the Chebyshev polynomial (interpolation points) are equispaced. Under this assumption, the N-order Chebyshev approximant is shown to converge ultimately to the cardinal one, as N goes to infinity, and to be practically indistinguishable from this latter, within the prescribed approximation level, already for N ~ 100 . [1] R.P. Croce et al., Phys. Rev. D62 (2000) 124020. [2] R.P. Croce et al., Phys. Rev. D62 (2000) R.121101. [3] D. Slepian, Proc. IEEE 64 (1976) 292. [4] V.A. Kotel’nikov, Izd. Red. Upr. Svyazi RKKA, Moscow, 1933. [5] S. Mitra et al., Phys. Rev. D72 (2005) 102001.