Study and Design of Second-Order Differential Arrays - Study and Design of Differential Microphone Arrays - page 90

80 80

60 60

40 40

20 20

0 0

0 ◦ 60 ◦ 120 ◦ 180 ◦ 240 ◦ 300 ◦ 360 ◦

Θ N

0 ◦ 60 ◦ 120 ◦ 180 ◦ 240 ◦ 300 ◦ 360 ◦

Θ N

( a ) ( b )

80 80

60 60

40 40

20 20

0 0

0 ◦ 60 ◦ 120 ◦ 180 ◦ 240 ◦ 300 ◦ 360 ◦

Θ N

0 ◦ 60 ◦ 120 ◦ 180 ◦ 240 ◦ 300 ◦ 360 ◦

Θ N

( c ) ( d )

80 80

60 60

40 40

20 20

0 0

0 ◦ 60 ◦ 120 ◦ 180 ◦ 240 ◦ 300 ◦ 360 ◦

Θ N

0 ◦ 60 ◦ 120 ◦ 180 ◦ 240 ◦ 300 ◦ 360 ◦

Θ N

(e) (f)

FIG. 4.29 The gain of the second-order cardioid with one distinct null for a point noise
source, as a function of Θ N , for several frequencies and two values of Δ : (a) F =0 . 5 kHz,
Δ = 1 cm, (b) F =0 . 5 kHz, Δ = 2 cm, (c) F = 1 kHz, Δ = 1 cm, (d) F = 1 kHz, Δ = 2 cm,
(e) F = 3 kHz, Δ = 1 cm, and (f) F = 3 kHz, Δ = 2 cm.

2 ×

1 − e ωτ 0 (cos θ N + 1)

D NS,2 ( ω )=

2

16
7 e

− ωτ 0 / 2 − 9

− ωτ 0

e ωτ 0 cos θ N 1 −

7 e

. (4.49)

′

Figure 4.29 shows plots of G

NS,2 [ h

( ω )], as a function of θ N , for several fre-

quencies and two values of δ .