Solutions to Home Work 3


P83-28) An image is 1024*768 pixels with 3 bytes/pixel. Assume the image is uncompressed. How

long does it take to transmit it over a 56-kbps modem channel? Over a 1-Mbps cable modem? Over

a 10-Mbps Ethernet? Over 100-Mbps Ethernet?



The image is 1024*768*3 bytes or 2,359,296 bytes. This is 18,874,368 bits. At 56,000 bits/sec,

it takes about 337.042 sec. At 1,000,000 bits/sec, it takes about 18.874 sec.

At 10,000,000 bits/sec, it takes about 18.87 sec. At 100,000,000 bits/sec, it takes about 0.819 sec.



P83-29) Ethernet and wireless networks have some similarities and some differences. One property of

Ethernet is that only one frame at a time can be transmitted on an Ethernet. Does 802.11 share

this property with Ethernet? Discuss your answer.



Think about the hidden terminal problem. Imagine a wireless network of five stations, A

through E, such that each one is in range of only its intermediate neighbours. Then A can talk

to B at the same time D is talking to E. Wireless networks have potential parallelism, and in this

way differ from Ethernet.



P177-1) Compute the Fourier coefficients for the function f(t) = t, (0<=t<= 1).



an = -1/п n,  bn = 0, c = 1.



p177-2) A noiseless 4-kHZ channel is sampled at every 1 msec. What is the maximum data rate?



A noiseless channel can carry an arbitrarily large amount of information, no matter how often

it is sampled. Just send a lot of data per sample. For the 4 kHz channel, make 8000 samples/sec.

If each sample is 16 bits, the channel can send 128 kbps. If each sample is 1024 bits, the

channel can send 8.2 Mbps. The key word here is "noiseless". With a normal 4 kHz channel, the

Shannon limit would not allow this.


p177-3) Television channels are 6 MHz wide. How many bits/sec can be sent if four-level digital

signals are used? Assume a noiseless channel.



Using Nyquist theorem, we can sample 12 million times/sec. Four-level signals provide 2 bits

per sample, for a total data rate of 24 Mbps.