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

  Solution:

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. Sketch the spectrum of m(t) ii. Find and sketch the spectrum of the DSB-SC signal 2𝑚(𝑡) cos(1000𝜋𝑡).

iii. From the spectrum obtained in part (ii), suppress the LSB spectrum to obtain the USB spectrum.

iv. Knowing the USB spectrum in part (ii), write the expression 𝜑!"#(𝑡) for the USB signal.

v. Repeat part (iii) and (iv) to obtain the LSB signal 𝜑!"#(𝑡).

Solution:

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

  Solution:

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

Solution:

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.