B. P. Lathi, Zhi Ding - Modern Digital and Analog Communication Systems-Oxford University Press (2009)

70 ANALYSIS AND TRANSMISSION OF SIGNALS
Fi g ure 3.6
Rectangular
pulse.
II (x)
II ({ )
-1
2
0
(a)
1
2
x--.
-'t
2
(b)
0
't
2
Fi g ure 3.7
Triangular pulse.
L'.l(x)
-1
2
(a)
0
1 x--.
-'t
0
(b)
't
Unit Rectangular Function
We use the pictorial notation IT (x) for a rectangular pulse of unit height and unit width, centered
at the origin, as shown in Fig. 3.6a:
IT(x) - { 5
lxl :::: ½
lxl = ½
lxl > ½
(3.16)
Notice that the rectangular pulse in Fig. 3.6b is the unit rectangular pulse IT (x) expanded
by a factor r and therefore can be expressed as IT(x/r). Observe that the denominator r in
IT (x / r) indicates the width of the pulse.
Unit Triangular Function
We use the pictorial notation Ll (x) for a triangular pulse of unit height and unit width, centered
at the origin, as shown in Fig. 3.7a:
1 1 - 21tl lxl < ½
Ll(x) =
(3.17)
lxl > ½
Observe that the pulse in Fig. 3.7b is Ll(x/r). Observe that here, as for the rectangular pulse,
the denominator r in Ll(x/r) indicates the pulse width.
Sine Function sinc(x)
The function sin x/x is the "sine over argument" function denoted by sine (x).*
* sine (x) is also denoted by Sa (x) in the literature. Some authors define sine (x) as
sin nx
nx
sine (x) = --