Page 152 - Fundamentals of Communications Systems

4.28 Chapter Four

X f() X f()
c c
A A

2A
3
A
3

f
f c c
arg X f (){ } arg X f (){ }
π c π c

π π
2 2

f f
c c
π π
− −
2 2

−π −π
Figure 4.25 Amplitude and phase of a bandpass signal.

Problem 4.23. If F{x z (t)}= X z (f ) what is F{x (t)}?
∗
z
Problem 4.24. An often used pulse in radar systems has a complex envelope of

2
⎧
⎨A c exp[ j 2πg 0 t ]0 ≤ t ≤ T p
x z (t) = (4.51)
0 elsewhere
⎩
(a) What are x A (t) and x P (t).
(b) Plot the bandpass signal, x c (t) for f c = 10 Hz and g 0 = 100 Hz/s, A c = 1,
and T p = 1.
?
(c) What is the E x z
(f ) and estimate B 98 when g 0 = 100 Hz/s and T p = 1.
(d) Plot G x z
Problem 4.25. A complex baseband signal is given as x z (t) = x I (t)+ jx Q (t), where
x I (t) and x Q (t) are real lowpass signals. Find