IT 420 Fall 2017 Homework 2 Note: Where applicable, units of the solution must b

Question

IT 420

Fall 2017

Homework 2

Note: Where applicable, units of the solution must be correct for full credit.

1.Answer the following questions:

1.1   A signal has 1000 possible levels. This signal is

a.analog b. digital         c. neither        d. cannot be determined

           1.2 Taking too many samples while sampling may lead to

            a. too few bits in the quantization

            b. using too much bandwidth for PCM

            c. incorrectly reproducing the data

            d. a parity error

1.3 Which technique converts digital data to a digital signal?

            a. Line coding                        b. Shannon’s theorem                        c. Pulse Code Modulation

1.4 Channel capacity is

            a. the theoretical upper limit on how many bits/sec can pass through a link

            b. the number of samples/sec required for PCM

            c. the analog bandwidth

            d. the maximum baud rate of a link

1.5 Shannon’s theorem for channel capacity assumes a perfect channel.

a.True     b. False

2.A digital signal has 32 possible levels. How many bits are necessary to represent each level?

3.In a digital signal, one baud interval is 2ms. What is the baud rate?

4.A device is sending out data at the baud rate of 100 levels/sec and each level represents 8

bits. What is the data rate in bps?

5.What is a possible unit for each measurement?

a.Baud rate                           ___________________

b.Bit rate                              ___________________

c.Baud interval                     ___________________

d.Channel capacity               ___________________

6.Encode the data stream 1001101 using Manchester line coding. State any required assumptions (such as the value of the previous bit, if necessary) in your solution. Please be neat and show bit times.

7.An analog data signal contains frequencies from 1000 Hz to 3000 Hz. We wish to convert this to a digital signal using Pulse Code Modulation. Assume that there will be 64 possible quantized values.

What is the minimum sampling rate according to the Nyquist Theorem?

How many bits are required to represent each value?

Assuming the bits/sample and sampling rate calculated above, what is the bit rate?

8.What is the maximum channel capacity of a perfect channel which accepts frequencies between 100 MHz and 600 MHz and transmits a signal with 16 signal levels?

9.You need to send 360 Kbps over a perfect channel with an analog bandwidth of 30 KHz. How many signal levels do you need?

10.We currently have a noisy channel with an analog bandwidth of 100 MHz and a signal to noise ratio of 31 (not in dB) We need to upgrade the channel to a higher channel capacity. Answer the following questions.

a.What is the current capacity?

b. What do we have to change the bandwidth to in order to double the channel capacity?

11.Answer the following questions concerning error detection:

7.1 A receiver receives a message containing redundant bits for error checking and uses those bits to determine that no error has occurred. What does the receiver then do with the redundant bits?

a.discards them

b.returns them to the sender

c.passes them to the next layer up in the network model at the receiver

d.saves them for future use

7.2 Can single-bit parity detect an error that flips exactly two data bits?

            a. Yes             b. No              c. Sometimes - it depends on the data

7.3   Can row-and-column parity detect and correct a single bit error?

            a. Yes             b. No              c. Sometimes - it depends on the data

12.Assume even parity.

a.Data is 10101011. What is the parity bit?

b.A receiver receives data 10101010 and a parity bit of 1. Will the receiver accept or reject the data?

13.Assume odd row and column parity with 8 data bits per row. Show the parity bits for

11110111

01011001

Explanation / Answer

1.1 A signal has 1000 possible levels. This signal is
Ans: b)digital.

1.2 Taking too many samples while sampling may lead to
Ans: a. too few bits in the quantization

1.3 Which technique converts digital data to a digital signal?
Ans: a. Line coding

1.4 Channel capacity is
Ans: a. the theoretical upper limit on how many bits/sec can pass through a link
It is the upper bound of rate at which information

1.5 Shannon’s theorem for channel capacity assumes a perfect channel.
Ans: true.

2.A digital signal has 32 possible levels. How many bits are necessary to represent each level?
Ans: Number of bits per level = log2 n
=log2 32
= 5 bits

3.In a digital signal, one baud interval is 2ms. What is the baud rate?
baudrate is 9600bps

4.A device is sending out data at the baud rate of 100 levels/sec and each level represents 8
bits. What is the data rate in bps?
Data rate = 100 levels * 8 bits sec level = 800 bps

What is the minimum sampling rate according to the Nyquist Theorem?
the sampling rate must be at least 2fmax

7.1 receiver receives a message containing redundant bits for error checking and uses those bits to determine that no error has occurred. What does the receiver then do with the redundant bits?
Ans: c.passes them to the next layer up in the network model at the receiver

7.2 Can single-bit parity detect an error that flips exactly two data bits?
Ans: a. Yes   

7.3 Can row-and-column parity detect and correct a single bit error?
Ans: No

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