Question 1 Consider the FM radio frequencies between 89 and 93 MHz. (Remember th

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Question 1

Consider the FM radio frequencies between 89 and 93 MHz. (Remember that the bandwidth of an FM radio station is 200 KHz.) Seven Orlando stations operate in this range:

WLAZ

WPIO

WUCF

WMFE

WKES

WPRK

WWKA

89.1 FM

89.3 FM

89.9 FM

90.7 FM

91.1 FM

91.5 FM

92.3 FM

a) What are the smallest and largest frequencies transmitted by WKES FM?

b) How many more FM radio stations can operate in this same area, in the 89-93 MHz frequency range? Why?

c) If the entire bandwidth of one of these stations was used to transmit data in a noiseless channel with eight signal levels, according to Nyquist bit rate formula, what would be that channel's bit rate?

Question 2

A periodic composite signal contains sine harmonics with frequencies from 6 KHz to 54 KHz. All harmonics from 6-54 KHz, i.e., 6 KHz, 12 KHz, 18 KHz, 24 KHz, 30 KHz, 36 KHz, 42 KHz, 48 KHz, and 54 KHz, are included in the signal.

The signal is transmitted over a channel that has attenuation of -(infinity) dB for frequencies less than or equal to 18 KHz, and -4 dB for all frequencies greater than 18 KHz.

All harmonics have a maximum power of 60 mW at the sender's side of the channel. Recall the attenuation formulae is dB = 10 log10 (P2/P1).

a) How many harmonics reach the receiver?

b) What is their maximum power when received?

c) What is the bandwidth of the signal as sent?

d) What is the bandwidth of the signal as received?

Question 3 (4 points)

Consider a mesh network connecting n devices.

a) The total number of cables in the network is 55. What is n?

b) The link connecting two given devices has a bandwidth of 12 KHz and an SNR (signal-to-noise ratio) of 37. According to Shannon capacity formula, please calculate the theoretical capacity of this channel.

c) A sender S transmits fixed-length packets to a receiver R over a link in the network at 100 Kbps. The one-way propagation delay is 100ms. How much traffic, measured in bits, fills this link at a given time?

WLAZ

WPIO

WUCF

WMFE

WKES

WPRK

WWKA

89.1 FM

89.3 FM

89.9 FM

90.7 FM

91.1 FM

91.5 FM

92.3 FM

Explanation / Answer

1.
a) The smallest frequency transmitted by WKES is 91.1 – 0.1 = 91.0 MHz
The largest frequency transmitted by WKES is 91.1 + 0.1 = 91.2 MHz

b) Total FM bandwidth allowed in the specified range = 89.0 – 93.0 = 4.0 MHz Maximum number of non-overlapping channels = 4 MHz / 0.2 MHz = 20 Channels

c) The channels is noiseless and we should use the Nyquist formula. Bit rate = 2 × BW × log 2 (L) = 2 × 200 KHz × log 2 (8) = 2 × 200 KHz × 3 = 1200KBPS= 1.2Mbps

2.

a) How many harmonics reach the receiver?
24 Khz, 30Khz, 36Khz, 42Khz, 46Khz, 54Khz

b) What is their maximum power when received?
- 4 dB = 10 log 10 (P 2 /P 1 ) P 2 /P 1 = 10 -0.3 = 0.25
P 1 = maximum power of the signal at the sender’s side = 54 mW
P 2 = maximum power of the signal at the receiver’s side = 0.25 × P 1 = 13.5 mW

c) What is the bandwidth of the signal as sent?

54-6=48KHz
d) What is the bandwidth of the signal as received?
54-18=36KHz

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