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It is shown in a technical report by the author (2010c) that the maximum directivity index for this discriminating function is equal to Dmax = 4 a+1 a−1 (66) 31 Direction-Selective Filters for Sound Localization and is achieved when d0 and d1 have the values d0 = a−1 ( a − 3) 4 (67) d1 = a−1 ( 3a − 1) 4 (68) Note that the directivity given by Eq. (66) is four times the directivity given by Eq. (38). Analogous to Eqs. 105, Q = 10 and the maximum directivity index is 19 dB which is a 6 dB improvement over that of the first-degree discriminating function of Eq.
Evora, V. M. & Nuttall, A. H. (2003). Highly directional acoustic receivers, J. Acoust. Soc. , Vol. 13, No. 3, pp. 1526-1532. D’Spain, G. ; Hodgkiss, W. ; Edmonds, G. ; Nickles, J. ; Fisher, F. ; & Harris, R. A. (1992). Initial analysis of the data from the vertical DIFAR array, Proc. Mast. Oceans Tech. (Oceans ’92), pp. 346-351. D’Spain, G. ; Luby, J. ; Wilson, G. R. & Gramann R. A. (2006). Vector sensors and vector sensor line arrays: comments on optimal array gain and detection, J. Acoust.
Located at the origin is a directional acoustic sensor. , 2006) 3 po ( t ) = a0 p ( t ) + ρ0c ∑ a j ⎡⎣υ j ( t ) + n j ( t ) ⎤⎦ cos β j j =1 (1) The components of the look direction are the direction cosines cos β j , j = 1, 2, 3 where cos β 1 = cos θL sin φL cos β 2 = sin θ L sin φ L (2) cos β 3 = cos φL where the angles θ L is the azimuthal angle and φL the polar or zenith angle. The time function p ( t ) is the acoustic pressure at the origin and υ j ( t ) , j = 1, 2, 3 the three orthogonal components of the acoustic particle velocity.