Page 150 - Fundamentals of Communications Systems

4.26 Chapter Four

(c) If x z (t) = exp( j 2π f m t) find x c (t).
(d) If x z (t) = exp( j 2π f m t) compute y z (t) for 2000 ≤ f m < 9000.
Problem 4.17. Consider two bandpass filters

⎧
⎪ 1
⎨ √ 0 ≤ t ≤ 0.2
h z1 (t) = 0.2 (4.46)
⎪
0 elsewhere
⎩
sin(10πt)
h z2 (t) = (4.47)
10πt
Consider the filters and an input signal having a complex envelope of x z (t) =
exp( j 2π f m t).
(a) Find x c (t).
(b) Find H z (f ).
(c) Find H c (f ).
(d) For f m = 0, 7, 14 Hz find y z (t).

Problem 4.18. Find the amplitude signal, x A (t), and phase signal, x P (t) for
(a) x z (t) = z(t) exp( j φ) where z(t) is a complex valued signal.
(b) x z (t) = m(t) exp( j φ) where m(t) is a real valued signal.

Problem 4.19. A bandpass signal has a complex envelope given as
x z (t) = j exp[− j 2π f m t] + 3 exp[ j 2π f m t] (4.48)

where f m > 0.
(a) Find x I (t) and x Q (t).
(b) Plot the frequency domain representation of this periodic baseband signal
using impulse functions.
(c) Plot the frequency domain representation of the bandpass signal using
impulse functions.
(d) What is the bandpass bandwidth of this signal, B T ?

Problem 4.20. The amplitude and phase of a bandpass signal is plotted in
Figure 4.24. Plot the in-phase and quadrature signals of this baseband rep-
resentation of a bandpass signal.

Problem 4.21. A bandpass signal has a complex envelope given as
x z (t) = j exp[− j 2π f m t] + 3 exp[ j 2π f m t] (4.49)