Solution 6 - UAkron Blog

University of Akron
Department of Electrical and Computer Engineering
4400 341: Introduction to Communication Systems - Spring 2015
Assignment – 6 Solutions
5.4-3
Let s(t) be an angle-modulated signal that receiver obtains,
𝑠 𝑡 = 2 cos[10! 𝜋𝑡 + 2 sin 2000𝜋𝑡 + 0.3𝜋 − 3𝜋 cos(100𝑡)]
a) Find the bandwidth of this FM signal
b) If s(t) is sent to an (ideal) envelope detector, find the detector output signal.
c) If s(t) is first differentiated before the envelope detector, find the detector output
signal.
d) Explain which detector output can be processed to yield the message signal m(t)
and find the message signal m(t) if kf = 200π.
Solution:
5.6-1 A transmitter transmits an AM signal with a carrier frequency of 1530 kHz. When an
inexpensive radio receiver (which has a poor selectivity in its RF-stage bandpass filter) is
tuned to 1530 kHz, the signal is heard loud and clear. This same single is also heard (not
as strongly) at another dial setting. State, with reasons, at what frequency you will hear
this station. The IF frequency is 455 kHz.
Solution:
6.1-1 Figure 1 shows the Fourier spectra of signals g1(t) and g2(t). Determine the Nyquist
intervals and the sampling rate for the signals g1(t), g2(t), g12(t) , g2m(t), and g1(t)g2(t).
Hint: Use the frequency convolution and the width property of convolution
Figure 1
Solution:
6.1-5 Signals 𝑔! 𝑡 = 10! Π(10! 𝑡) and 𝑔! 𝑡 = 𝛿(𝑡) are applied at the inputs of ideal lowpass filters 𝐻! 𝑓 = Π(𝑓 20,000) and 𝐻! 𝑓 = Π(𝑓 10,000) as shown in Figure 2.
The outputs y1(t) and y2(t) of these filters are multiplied to obtain the signal 𝑦 𝑡 =
𝑦! (𝑡)𝑦! (𝑡). Find the Nyquist rate of y1(t), y2(t), and y(t). Use the convolution property
and the width property of convolution to determine the bandwidth of y1(t)y2(t).
Figure 2
Solution: