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University of Akron
Department of Electrical and Computer Engineering
4400 341: Introduction to Communication Systems - Spring 2015
Assignment – 4
4.3-3
For the AM signal with m(t) shown in Figure 1, and µ = 0.75:
a) Find the amplitude and power of the carrier.
b) Find the sideband power and the power efficiency, η.
Figure 1
4.4-2 A modulating signal m(t) is given by:
a) 𝑚 𝑡 = cos 100𝜋𝑡 + 2 cos(300𝜋𝑡)
b) 𝑚 𝑡 = sin 100𝜋𝑡 sin(500𝜋𝑡)
In each case:
i.
ii.
iii.
iv.
v.
Sketch the spectrum of m(t)
Find and sketch the spectrum of the DSB-SC signal 2𝑚(𝑡) cos(1000𝜋𝑡).
From the spectrum obtained in part (ii), suppress the LSB spectrum to obtain the
USB spectrum.
Knowing the USB spectrum in part (ii), write the expression 𝜑!"# (𝑡) for the USB
signal.
Repeat part (iii) and (iv) to obtain the LSB signal 𝜑!"# (𝑡).
4.5-2 Consider a VSB amplitude modulation system. The baseband signal is an audio signal of
the bandwidth 4 kHz. The carrier frequency is 1500 kHz. Suppose that the transmission
vestigial filter Hi(f) has a (symmetric) frequency response as shown in Figure 2.
a) Design and illustrate a receiver system block diagram.
b) Find the bandwidth of this transmission.
c) Describe and sketch the necessary equalizer filter response H0(f) for distortionless
reception.
Figure 2
5.1-2 A baseband signal m(t) is the periodic sawtooth signal shown in Figure 3.
a) Sketch 𝜑!" (𝑡) and 𝜑!" (𝑡) for this signal m(t) if 𝜔! = 2𝜋10! , 𝑘! = 2000𝜋, and
𝑘! = 𝜋 2.
b) Show that this PM signal is equivalent to another PM signal modulated by a periodic
rectangular message signal. Explain why it is necessary to use kp < π in this case.
[Note that the PM signal has a constant frequency but has phase discontinuities
corresponding to the discontinuities of m(t).]
Figure 3
5.1-4 Over and interval 𝑡 ≤ 1, an angle-modulated signal is given by
𝜑!" 𝑡 = 10 cos(13,000𝜋𝑡)
It is known that the carrier frequency, 𝜔! = 10,000𝜋.
a) Assuming a PM signal with 𝑘! = 1000. Determine m(t) over the interval 𝑡 ≤ 1.
b) Assuming an FM signal with 𝑘! = 1000. Determine m(t) over the interval
𝑡 ≤ 1.