Question

4. (25 points) Modulation and Demodulation (a) (10 points) Consider the communication system shown below: m(t) x(t) X H(j?) y(t) Propagation y(t) y(t) z(t) 42 m(t) X ? cos(?ct) Ideal Bandpass Ideal Lowpass cos(?ct) Transmitter Receiver The signal m(t) is first modulated by cos(?ct), and then passed through an ideal band- pass filter. The spectrum of the input M(j?) and the frequency response of the ideal bandpass filter H(j?) are: M(j?) -?c -2?B 2?B ?c ? 2?B 2?B H(j?) 1 -?c ?c The modulated signal is x(t), and the output of the ideal bandpass is y(t). This signal is transmitted through a channel. We assume that this channel does not introduce distortion into y(t). The received signal y(t) is then processed by a receiver. Sketch the signal spectrum at i. the output of the modulator, i.e., X(j?), ii. the output of the ideal bandpass, Y(j?), and iii. the output of the demodulator, Z(j?) Does this system recover m(t)?

          4. (25 points) Modulation and Demodulation
(a) (10 points) Consider the communication system shown below:
m(t)
x(t)
X
H(j?)
y(t) Propagation y(t)
y(t)
z(t)
42
m(t)
X
?
cos(?ct)
Ideal Bandpass
Ideal Lowpass
cos(?ct)
Transmitter
Receiver
The signal m(t) is first modulated by cos(?ct), and then passed through an ideal band-
pass filter. The spectrum of the input M(j?) and the frequency response of the ideal
bandpass filter H(j?) are:
M(j?)
-?c
-2?B
2?B
?c ?
2?B
2?B
H(j?)
1
-?c
?c
The modulated signal is x(t), and the output of the ideal bandpass is y(t). This signal
is transmitted through a channel. We assume that this channel does not introduce
distortion into y(t). The received signal y(t) is then processed by a receiver. Sketch the
signal spectrum at
i. the output of the modulator, i.e., X(j?),
ii. the output of the ideal bandpass, Y(j?), and
iii. the output of the demodulator, Z(j?)
Does this system recover m(t)?

4. (25 points) Modulation and Demodulation
(a) (10 points) Consider the communication system shown below:
m(t)
x(t)
X
H(j?)
y(t) Propagation y(t)
y(t)
z(t)
42
m(t)
X
?
cos(?ct)
Ideal Bandpass
Ideal Lowpass
cos(?ct)
Transmitter
Receiver
The signal m(t) is first modulated by cos(?ct), and then passed through an ideal band-
pass filter. The spectrum of the input M(j?) and the frequency response of the ideal
bandpass filter H(j?) are:
M(j?)
-?c
-2?B
2?B
?c ?
2?B
2?B
H(j?)
1
-?c
?c
The modulated signal is x(t), and the output of the ideal bandpass is y(t). This signal
is transmitted through a channel. We assume that this channel does not introduce
distortion into y(t). The received signal y(t) is then processed by a receiver. Sketch the
signal spectrum at
i. the output of the modulator, i.e., X(j?),
ii. the output of the ideal bandpass, Y(j?), and
iii. the output of the demodulator, Z(j?)
Does this system recover m(t)?

Added by Scott B.

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