Study and Design of First-Order Differential Arrays - Study and Design of Differential Microphone Arrays - page 55

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. 3.21 The gain of the first-order supercardioid for a point noise source, as a function
of Θ N , for several frequencies and two values of Δ : (a) Ω =0 . 125 Π , Δ = 1 cm, (b) Ω =0 . 125 Π ,
Δ = 2 cm, (c) Ω =0 . 5 Π , Δ = 1 cm, (d) Ω =0 . 5 Π , Δ = 2 cm, (e) Ω = Π , Δ = 1 cm, and (f)
Ω = Π , Δ = 2 cm.

Let us denote by θ S , the steering angle. The beampattern of the N th-order
DMA is now

N

a N,n cos n ( θ − θ S ) .

B

N ( θ,θ S )=

(3.57)

n=0