ENSC327 Communication Systems

Solution to Assignment #5

Question 2:

The positive part of the spectrum is plotted in the following figure for .

0.99 0.992 0.994 0.996 0.998 1 1.002 1.004 1.006 1.008 1.01

x 106

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

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4. Frequency Division Multiplexing

Solution:

The additional signals caused by the nonlinearity of the system can be too close to one of the desired signals and require

more precise filters ( more expensive and complicated to build) for extracting the desired signals.

If 𝜔1 and 𝜔2 are harmonics, some of the undesired signals can completely overlap with the desired signals. For

example if 𝜔2 = 2 𝜔1, then the signal at 2 𝜔1 will overlap with the desired signal centered at 𝜔2.

5. FM Generation

Solution:

6. Energy Spectral Density

7. Simulink: FM Modulator

Solution:

m

mf

m

mf

m A

fk

f

Ak

f

f

From Carlson’s rule, for single tone message, the FM bandwidth

112

11222 mfmT AkfffB

1) ,500,1 HzfA mm

1503.0 fk , 1300TB Hz

5001 fk , 2000TB Hz

12004.2 fk , 3400TB Hz

25005 fk , 6000TB Hz

2) 500fk

11 mA , 2000TB Hz

22 mA , 3000TB Hz

33 mA , 4000TB Hz