Digital Signal Processing Reference
In-Depth Information
The sample space is infinite but countable:
S ¼ fs
1
; s
2
; s
3
; s
4
; ...g:
(1.9)
Event
A
is formed by (
1.6
) and (
1.7
):
A ¼ fs
1
; s
2
; s
3
; s
4
g:
(1.10)
1.1.1 Operations with Events
The
complement
of an event
A
-denoted as
A
-is an event which contains all sample
point
s
not in
A
. For example, the complement of the event
A
in Fig.
1.1a
is the event
B ¼ A ¼ f
T
g
.
The
union
(or
sum
) of events
A
and
B
-denoted as
A[B
-is an event which
contains all points in
A
and
B
. For example, the union of the events
A
and
B
in
Fig.
1.1a
is:
A[B ¼
{H, T}. The union is also denoted as
A þ B
.
Fig. 1.4
Illustration of operations with events. (
a
) Complement. (
b
) Intersection. (
c
) Union.
(
d
) Disjoint events
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