Introduction - Study and Design of Differential Microphone Arrays - page 8

4 3 2 1

δ δ δ

z −Τ 1 z −Τ 1 z −Τ 1

− + − + − +

First-order
output

First-order
output

First-order output

z −Τ 2 z −Τ 2

− + − +

Second-order output Second-order

output

z −Τ 3

− +

Third-order output

FIG. 1.4 A schematic diagram of construction of first-, second-, and third-order DMAs.

sequently, it is necessary to perform frequency and level equalization to its
response according to the range and incident angle of the sound source [16].
However, this equalization process, though theoretically feasible, is in general
very di�cult for a DMA with an order higher than two. Finally, a DMA suf-
fers greatly from white noise amplification, particularly at low frequencies.
Although some efforts in the literature have been devoted to solving these
issues, they have not been fully addressed.
In summary, DMAs have the great potential to solve many important
problems in voice communication. However, unlike the additive arrays that
have been intensively studied in the past, differential arrays are less addressed
so far. Many aspects of DMAs are still unclear if not a mystery. This topic
is, therefore, devoted to providing a systematic study of DMAs from a signal
processing perspective. The primary objective is to develop fundamental the-
ory and algorithms associated with the design and implementation of DMAs
as well as principles to analyze and explain their performance and limitations.
Coverage of the theory includes signal processing algorithms for the design of
commonly used first-order, second-order, third-order, as well as the general
N th-order DMAs. For each order of DMAs, particular examples are given on
how to form standard directivity patterns such as the dipole, cardioid, super-
cardioid, hypercardioid, subcardioid, and quadrupole. Study is also provided
to show the performance of different order DMAs and the related beamform-
ing algorithms in terms of beampattern, directivity factor, white noise gain,
and gain for a point source. The inherent relationship between differential
beamforming and adaptive beamforming is discussed, which provides a dif-