Study and Design of First-Order Differential Arrays - Study and Design of Differential Microphone Arrays - page 43

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. 3.10 The gain of the first-order cardioid 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.

3.4 General First-Order Differential Array

We consider designing any first-order differential array with the linear system
of two equations:

1 e ωτ 0
1 e ωτ 0 α 1,1

1
β 1,1

h ( ω )= , (3.34)