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Table 1 Values of the vector b2N of the first-, second-, and third-order dipole, cardioid, supercardioid, and hypercardioid

From: Steerable differential beamformers with planar microphone arrays

  N b2N
Dipole 1 \(\mathbf {b}_{2N} = \left [ \frac {1}{2}~~ 0~~ \frac {1}{2} \right ]^{T}\)
  2 \(\mathbf {b}_{2N} = \left [ \frac {1}{4}~~0~~\frac {1}{2}~~ 0~~ \frac {1}{4} \right ]^{T}\)
  3 \(\mathbf {b}_{2N} = \left [ \frac {1}{8}~~0~~\frac {3}{8}~~ 0~~ \frac {3}{8}~~0~~ \frac {1}{8} \right ]^{T}\)
Cardioid 1 \(\mathbf {b}_{2N} = \left [ \frac {1}{4}~~ \frac {1}{2}~~ \frac {1}{4} \right ]^{T}\)
  2 \(\mathbf {b}_{2N} = \left [ \frac {1}{8}~~\frac {1}{4}~~ \frac {1}{4}~~ \frac {1}{4}~~ \frac {1}{8} \right ]^{T}\)
  3 \(\mathbf {b}_{2N} = \left [ \frac {1}{16}~~\frac {1}{8}~~\frac {3}{16}~~ \frac {1}{4}~~ \frac {3}{16}~~ \frac {1}{8}~~ \frac {1}{16} \right ]^{T}\)
Hypercardioid 1 \(\mathbf {b}_{2N} = \left [ \frac {1}{3}~~ \frac {1}{3}~~ \frac {1}{3} \right ]^{T}\)
  2 \(\mathbf {b}_{2N} = \left [ \frac {1}{5}~~ \frac {1}{5}~~ \frac {1}{5}~~ \frac {1}{5}~~ \frac {1}{5} \right ]^{T}\)
  3 \(\mathbf {b}_{2N} = \left [ \frac {1}{7}~~ \frac {1}{7}~~ \frac {1}{7}~~ \frac {1}{7}~~ \frac {1}{7}~~ \frac {1}{7}~~ \frac {1}{7} \right ]^{T}\)
Supercardioid 1 b2N≈[0.293 0.414 0.293]T
  2 b2N≈[0.1035 0.242 0.309 0.242 0.1035]T
  3 b2N≈[0.036 0.1185 0.216 0.259 0.216 0.1185 0.036]T