Problem 13
Television channels are \(6 \mathrm{MHz}\) wide. How many bits/sec can be sent if four-level digital signals are used? Assume a noiseless channel.
Problem 14
If a binary signal is sent over a \(3-\mathrm{kHz}\) channel whose signal-to- noise ratio is \(20 \mathrm{~dB}\), what is the maximum achievable data rate?
Problem 16
What is the minimum bandwidth needed to achieve a data rate of \(B\) bits/sec if the signal is transmitted using NRZ, MLT-3, and Manchester encoding? Explain.
Problem 17
Prove that in \(4 \mathrm{~B} / 5 \mathrm{~B}\) mapped data with the NRZI encoding, a signal transition will occur at least every four bit times.
Problem 18
A modem constellation diagram similar to Fig. 2-17 has data points at \((0,1)\) and \((0,2)\). Does the modem use phase modulation or amplitude modulation?
Problem 19
In a constellation diagram, all the points lie on a circle centered on the origin. What kind of modulation is being used?
Problem 20
Ten signals, each requiring \(4000 \mathrm{~Hz}\), are multiplexed onto a single channel using FDM. What is the minimum bandwidth required for the multiplexed channel? Assume that the guard bands are \(400 \mathrm{~Hz}\) wide.
Problem 23
Consider a different way of looking at the orthogonality property of CDMA chip se- quences. Each bit in a pair of sequences can match or not match. Express the orthogonality property in terms of matches and mismatches.
Problem 27
How many end office codes were there pre-1984, when each end office was named by its three-digit area code and the first three digits of the local number? Area codes started with a digit in the range \(2-9\), had a 0 or 1 as the second digit, and ended with any digit. The first two digits of a local number were always in the range \(2-9\). The third digit could be any digit.
Problem 28
A simple telephone system consists of two end offices and a single toll office to which each end office is connected by a 1-MHz full-duplex trunk. The average telephone is used to make four calls per 8-hour workday. The mean call duration is \(6 \mathrm{~min}\). Ten percent of the calls are long distance (i.e., pass through the toll office). What is the maximum number of telephones an end office can support? (Assume \(4 \mathrm{kHz}\) per circuit.) Explain why a telephone company may decide to support a lesser number of telephones than this maximum number at the end office.
