ECE 380 Introduction to Communication Systems
Homework Assignment 5 Due: No need to submit
Problem 1. The message signal m(t), whose Fourier transform is shown in Figure 1, is transmitted from Point A to Point B.
Figure 1: Frequency spectrum for the message in Problem 2.
a) If LSSB AM is employed, what is the bandwidth of the modulated signal?
b) If DSB-SC AM is employed, what is the bandwidth of the modulated signal?
c) If conventional AM is employed where ka = 0.8, what is the bandwidth of the modulated signal?
Problem 2. An SSB-AM signal is generated by modulating an 10kHz carrier by the message signal
m(t) = 2Bsinc2(2Bt),
where B =2kHz. The amplitude of the carrier is Ac = 100.
a) mˆ (t) is the Hilbert transform of m(t). Draw the frequency spectrum (both magnitude spectrum
and phase spectrum) of mˆ (t).
b) Find SUSSB(f), the Fourier transform of the USSB AM signal. Draw its the magnitude spectrum.
Problem 3. A QAM system is shown in Figure 2. Consider m1(t) = sinc(t) and m2(t) = sinc2(t).
Figure 2: A QAM system in Problem 4.
a) Find φQAM (t) and its bandwidth in Hz.
b) Find the required bandwidth for the low-pass filters at the receiver.
c) If m2(t) = 12 sinc2(2t), repeat parts (a) and (b).
d) what does happen if m2(t) is the Hilbert transform of m1(t)? Comment on the type of the
modulation of φQAM (t).
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