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
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.