Introduction - Study and Design of Differential Microphone Arrays - page 5

50

40

30

20

10

0

◦ ◦

40 ◦

◦

80 ◦

◦ ◦

140 ◦

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0 20 60 100 120 160 180

Incident angle θ N

FIG. 1.2 Gain in SNR of the DS beamformer with a uniformly spaced linear array for a
point noise source with incident angle Θ N . M = 10, Θ = 90 ◦ , Δ = 8 cm, and F = 2 kHz.

◦

Figure 1.3 plots the beampattern when M = 10, δ = 8 cm, θ S = 90

, and
f = 2 kHz. It consists of a total of nine beams 1 . The one with the high-
est amplitude is called the main lobe and all the others are called side lobes.
One important parameter regarding the main lobe is the so-called beamwidth
(or main lobe width), which is defined as the region between the first zero-
crossings on either side of the main lobe. For a DS beamformer with a linear
array, the beamwidth is 2 cos −1 [ c/ ( Mfδ )]. The beampattern of Fig. 1.3 in-
dicates that the DS beamformer allows the desired signal from the look di-
rection (i.e., θ = θ S ) to pass through without attenuation, while suppressing
noise and other interfering signals coming from other directions. The degree
of suppression depends on the number of sensors, the microphone spacing,
the angular separation between the desired signal and the signals to be sup-
pressed, and frequency.
The above simple DS beamformer, though illustrated with a linear ar-
ray, can be used in any geometry of arrays such as the circular, planar, and
spherical ones. However, the use of a DS beamformer to process broadband
speech signals suffers from the following number of problems and drawbacks.
1) Its beampattern is frequency dependent and the beamwidth is inversely
proportional to the frequency. Therefore, this beamformer is not effective in
dealing with low-frequency noise and interference. 2) Noise is not uniformly
attenuated over its entire spectrum, resulting in some disturbing artifacts in
the array output [6]. 3) If the incident angle of the speech source is different
from the array look direction, even slightly, the speech signal will be low-pass
filtered, leading to speech distortion. To overcome these drawbacks, broad-
band beamforming techniques have been developed with the subband and
filter-and-sum frameworks [7], [8]. In the former structure, the array signals

1 For a properly designed array, the number of beams in the range between 0 ◦ and 180 ◦
is equal to M − 1.