Introduction - Study and Design of Differential Microphone Arrays - page 6

90 ◦

120 ◦

60 ◦

30 ◦

150 ◦

180

◦

0

◦

0 − 10 − 20 − 30 − 40 − 40 − 30 − 20 − 10 0

dB
FIG. 1.3 Beampattern of the DS beamformer with a uniformly spaced linear array. M =
10, Θ S = 90 ◦ , Δ = 8 cm, and F = 2 kHz.

are decomposed into multiple subbands. A narrowband beamformer is de-
signed in each subband with a constraint applied to control the beamwidth so
that all the beamformers from different subbands have the same beamwidth.
Though it can make constant beamwidth across a wide range of frequen-
cies, this way of broadband beamforming sacrifices the array performance in
high frequencies. In comparison, the filter-and-sum structure applies a finite-
impulse-response (FIR) filter to each sensor signal and then sums up all the
filtered signals to form the array output. The core problem in this broad-
band beamforming is to determine the coe†cients of those FIR filters, which
can be accomplished either independently of the acoustic environment and
array data (fixed beamformer) or in an adaptive manner according to the
received array data such as the minimum variance distortionless (MVDR)
and linearly constrained minimum variance (LCMV) algorithms [7], [9]-[14].
Generally speaking, adaptive beamformers can be more e†cient than the
fixed ones in suppressing reverberation and competing sources; but they may
suffer from desired signal cancellation, which deserves careful attention.
Additive arrays have been intensively studied in the literature. For the
interested reader, see [2], [4], [5] for a more comprehensive coverage of such
arrays and their processing algorithms. In general, additive arrays are large
in size and they may be effective in processing high frequency signals while
they may not be at low frequencies.
Differential microphone arrays (DMAs) refer to the arrays that are respon-
sive to the spatial derivatives of the acoustic pressure field. The basic idea of
such arrays can be traced back to the 1930s when the directional ribbon mi-
crophones were invented [15], [16]. The earliest such directional microphones
were constructed by combining omnidirectional pressure sensors and gradient
ribbon sensors 2 together to produce the desired directional patterns such as
the dipole, cardioid, hypercardioid, and supercardioid. This idea was then

2 Note that ribbon microphones are gradient sensors in nature because they directly mea-
sure the sound pressure gradient and not the sound pressure itself.