13 where M = m$_{1}$ + m$_{2}$ is the total mass of the compact binary, µ = m$_{1}$m$_{2}$/M is the reduced mass and η = µ/M . µ = 1 16 f 2 a ( 5 4 π $^{4}$τ$_{0}$ τ 2 1 . $_{5}$) 1 / 3 , (A5) 5 τ$_{1}$$_{.}$$_{5}$ M = 32 f$_{a}$ π $^{2}$τ$_{0}$ , (A6) allowing τ$_{1}$ and τ$_{2}$ to be obtained algebraically from τ$_{0}$ and τ$_{1}$$_{.}$$_{5}$ . 2. The phase function In Eq. 3, the function ψ ( f ; θ ) is given by, ψ ( f ; θ ) = ∑ i ∈{ 0 , 1 , 1 . 5 , 2 } α$_{i}$ ( f ) τ$_{i}$ , (A7) α$_{0}$ ( f ) = 2 πf − 16 πf$_{a}$ 5 + 6 πf$_{a}$ 5 ( f f$_{a}$ ) − 5 / 3 , (A8) α$_{1}$ ( f ) = 2 πf − 4 πf$_{a}$ + 2 πf$_{a}$ ( f f$_{a}$ ) − 1 , (A9) α$_{1}$$_{.}$$_{5}$ ( f ) = − 2 πf + 5 πf$_{a}$ − 3 πf$_{a}$ ( f f$_{a}$ ) − 2 / 3 , (A10) α$_{2}$ ( f ) = 2 πf − 8 πf$_{a}$ + 6 πf$_{a}$ ( f f$_{a}$ ) − 1 / 3 . (A11) The chirp-time parameters, { τ$_{a}$ } , a = 0 , 1 , 1 . 5 , 2, are given in terms of the masses, m$_{1}$ and m$_{2}$ ≤ m$_{1}$ , of the binary components (we use c = G = 1), 1. Chirp-time parameters Appendix A: Details of the signal waveform τ$_{0}$ = 5 256 M − 5 / $^{3}$η − $^{1}$( πf$_{a}$ ) − 8 / 3 , (A1) τ$_{1}$ = 5 192 µ ( πf$_{a}$ ) 2 ( 743 336 + 11 4 η ) , (A2) τ$_{1}$$_{.}$$_{5}$ = 1 8 µ M 5 ) 1 / 3 , (A3) τ$_{2}$ = 5 128 µ ( M π $^{2}$f$_{a}$ 2 ) 2 / 3 ( 3058673 1016064 + 5429 1008 η + 617 144 η 2 ) , (A4) [2] A. Wainstein and V.D. Zubakov, Extraction of Signals from Noise (Prentice-Hall, Englewood Cliffs, 1962). [3] B. J. Owen, Phys. Rev. D 53 , 6749 (1996). [1] C.W. Helstrom, Statistical Theory of Signal Detection , 2nd ed. (Pergamon Press, London, 1968). [4] S. D. Mohanty and S. V. Dhurandhar, Phys. Rev. D 54 , 7108 (1996). [5] B. J. Owen and B. S. Sathyaprakash, Phys. Rev. D 60 , 022002 (1999). Since all the chirp time parameters depend on m$_{1}$ and m$_{2}$ , only two of them are independent. It is convenient to choose τ$_{0}$ and τ$_{1}$$_{.}$$_{5}$ as the independent parameters since M and µ can be obtained algebraically from them, [6] S. D. Mohanty, Phys. Rev. D 57 , 630 (1998). [7] A. S. Sengupta, S. V. Dhurandhar, A. Lazzarini, Phys. Rev. D 67 , 082004 (2003). [8] N. Christensen, R. Meyer and A. Libson, Class. Quantum Grav. 21 317 (2004). [9] N. Cornish and J. Crowder, Phys. Rev. D 72 , 043005 (2005). [10] E. Wickham, A. Stroeer, A. Vecchio, Class. Quantum Grav. 23 , S819 (2006). [11] J. Kennedy and R. C. Eberhart, Particle swarm opti- mization , in Proc. IEEE Int. Conf. Neural Networks, Pis- cataway, NJ, vol. 4, pp. 1942 – 1948 (Nov. 1995). Online at IEEE Xplore, URL: http://ieeexplore.ieee.org [12] See the articles in Proc. IEEE Swarm Intelligence Sym- posium, Nashville, TN, USA ( March 30 - April 2, 2009 ). Online at IEEE Xplore, URL: http://ieeexplore.ieee.org [13] B P Abbott et al , Rep. Prog. Phys. 72 , 076901 (2009). [14] The design sensitivity curve is available as a text file from the URL: http://www.ligo.caltech.edu/ ∼ jzweizig/distribution/LSC Data/ [15] L. Blanchet, T. Damour, B. R. Iyer, C. M. Will, and A. G. Wiseman, Phys. Rev. Lett. 74 , 3515 (1995). [16] B. S. Sathyaprakash, Phys. Rev. D 50 , R7111 (1994). [17] S. Droz, D. J. Knapp, E. Poisson, B. J. Owen, Phys. Rev. D 59 , 124016 (1999). [18] J. Robinson and Y. Rahmat-Samii, IEEE Trans. Anten- nas and Propagation, 52 , no. 2, 397 (2004). [19] R. R. Wilcox, Introduction to Robust Estimation and Hy- pothesis Testing , 2 nd Edition (Academic Press, 2005). [20] R. Balasubramanian, B. S. Sathyaprakash and S. V. Dhu- randhar, Phys. Rev. D 53 , 3033 (1996). [21] S. Babak et al , Class. Quantum Grav. 25 , 114037 (2008). The functions α$_{a}$ , a = 0 , 1 , 1 . 5 , 2 and the f − 7 / 6 factor in the amplitude of the signal (Eq. 3) can be pre-computed and stored, reducing the computational cost of generat- ing waveforms.