CS/ECE 757 Fall 2007
Homework 1 Solution
Instructions:
• Be sure to write your name on your submission.
• Show all your steps and state your assumptions.
• Complete the homework individually.
• Pledge: On my honor as a student I have neither given nor received aid on this exam/assignment.
(Write out and sign).
• The only help that you can get is from your class notes and the reference textbooks.
• Be neat. Unreadable solutions will not be graded.
• Number of problems: 7
• Total points: 30 points (will be scaled down for the final grade)
Due Date: Oct. 2, 2007 (submit in class, at the start of class)
Problem 1. [2 points]
Assume that the SNR of a received signal is 20dB, and that the bandwidth of the communication chan-
nel is 2.4kHz. What is Shannon’s channel capacity? [Do not forget the unit.]
Answer:
SNR is 20dB. Since , is 100, since . Given that W=2.4kHz,
we compute Shannon’s channel capacity as
Problem 2. (4 points):
A scanner has a resolution of pixels per square inch and creates 8 bits of data per pixel. This
scanner is used to scan an image into a data file. How long does it take to transfer this data file
across a 10km link? Assume that the transmission rate of the link is 100Mbps, and that the dielectric con-
stant of the medium is 1.7. Your answer should consider delays due to emission and propagation. Assume
no errors occur during the transfer, and there are no flow-control effects.
Answer:
Since the question asks for the time to send the data file across the link, we need to include both prop-
agation delay and emission (transmission) delay. The emission delay (time to emit the data file on to the
channel) is pipelined with the time to propagate all the bits except for the last bit. Hence we need to add
SNR dB() 10 SN⁄()
10
log=SN⁄() 100
10
log 2=
CH 1S
N
----
+
⎝⎠
⎛⎞
2
log 2400 1 100+()
2
log 2400 101()
10
log
2
10
log
-------------------------- 15980bits/sec== = =
600 600×
8″10″×
