Digital Signal Processing Reference
In-Depth Information
Figure 6.3
Probability density functions characterizing additive random sampling: (a),
(b), (c), (d) probability density functions of time intervals
t
1
−
t
0
,
t
2
−
t
0
,
t
3
−
t
0
and
t
7
−
t
0
respectively; (e) resulting sampling point density function
henceforth denoted
P
k
(
t
). These functions have their usual definitions. If the
probability density functions of the respective random time intervals are
p
k
(
t
),
then
∞
P
k
(
t
)
=
p
k
(
t
) d
t
.
(6.7)
0
}
form a basis of yet another very useful characteristic
of randomized sampling. This can be called the sampling function and can be
denoted
P
s
(
t
). This function was first introduced in the field of renewal theory,
where it was known as the renewal function, and can be defined as follows:
These functions
{
P
k
(
t
)
∞
P
s
(
t
)
=
P
k
(
t
)
.
(6.8)
k
=
1
