Page 144 - Fundamentals of Communications Systems

4.20 Chapter Four

xt ()
Q

045exp j [ 77°]
.
• Yellow
0 59exp j [ 151°]
.
• Green 064exp j [ 137°. ]
.
• Red
0 64exp j [ 193°] xt()
.
I
• Cyan
0 59exp j [ 331°]
.
• Magenta
0 45exp j [ 257°]
.
• Blue

Figure 4.14 Vector scope representation of the complex envelope
of the 3.58 MHz chrominance carrier.

(a) If the video picture is making a smooth transition from a blue color (at t =
0) to green color (at t = 1), make a plot of the waveforms x I (t) and x Q (t).
(b) Plot x I (t) and x Q (t) that would represent a scan across a red and green
striped area. For consistency in the answers assume the red starts at t = 0
and extends to t = 1, the green starts at t = 1 and extends to t = 2, ···.
+
Problem 4.6. Consider two lowpass spectra, X I (f ) and X Q (f ) in Figure 4.15 and
(f ).
sketch the energy spectrum of the complex envelope, G x z

I [
Re Xf ()] Im X ()]
[
f
Q
A
A
− f
1
−f f f
1 1 1
I [ −A
[
Im Xf ()] = 0 Re X ()] = 0
f
Q
Figure 4.15 Two lowpass Fourier transforms.