Digital Signal Processing Reference
In-Depth Information
1
M
=
500
l
g
r
,
y
i
d
.
,
©
,
L
s
M
=
20
M
=
5
−
39
−
26
−
13
0
13
26
39
Figure 8.1
Weighting function
w
k
(
M
)
in (8.14) as a function of
k
.
8.4.3 White Noise
A WSS random process
W
[
n
]
whose mean is zero and whose samples are
uncorrelated is called
white noise
. The autocorrelation of a white noise pro-
cess is therefore:
2
W
r
W
[
n
]=
σ
δ
[
n
]
(8.17)
2
where
W
is the variance (i.e. the expected power) of the process. The power
spectral density of a white noise process is simply:
σ
e
j
ω
)=
σ
2
W
(
P
W
(8.18)
Please note:
•
The probability distribution of a white noise process can be any, pro-
videdthatitisalwayszeromean.
•
The joint probability distribution of a white noise process need not be
i.i.d.; if it is i.i.d., however, then the process is strict-sense stationary
and it is also called a strictly white process.
•
White noise is an ergodic process, so that its pdf can be estimated
from a single realization.
8.5 Stochastic Signal Processing
In stochastic signal processing, we are considering the outcome of a filter-
ing operation which involves a random process; that is, given a linear time-
