Image Processing Reference
In-Depth Information
Data acquisition and
processing module
Communications
module
Microphone
Speech
source
Sensor
nodes
FIGURE .
Sensor network monitoring a stationary sound source in room.
To formulate this problem mathematically, we assume that the sound signal under observation,
called
x
,isarandomprocess.
∗
It is well known that a complete statistical description of a zero-
mean Gaussian wide-sense stationary (WSS) random process is provided by its “autocorrelation
sequence” (ACS)
(
n
)
)=
R
x
(
k
E
{
x
(
n
)
x
(
n
+
k
)}
or, equivalently, by its “power spectrum” also known as “power spectral density”
∞
∑
e
j
ω
e
−
j
ω
k
.
P
x
(
)=
R
x
(
k
)
k
=−∞
The ACS is a time-domain description of the second-order statistics of a random process. The power
spectrum provides a frequency domain description of the same statistics. Here, we are concerned with
determining the “power spectrum” of a random signal using distributed data obtained by a sensor
network.
†
∗
∗The reader is referred to the excellent texts [-] for basic introduction to random processes.
†
†The problem of estimating the power spectrum of a random signal when the signal itself is not available but some mea-
sured signals derived from it are observable has been studied in []. The approach developed in [], however, leads to a
centralized fusion algorithm, which is not suited to sensor network applications.
