Homework on Signal Characterization, 2000 version (solutions)

Feel free to work on the homework in groups. The work you hand in, however, should reflect your understanding of the material. You should show all of your calculations (neatly) and justify all of your answers for full credit.

You want to send your T-shirt order to SPS in the quickest manner. You, seeing a chance for appreciation of these collector's items, decide to order 25 of them.

1. What is the binary code for 25? 11001, since
1 * 2⁴ + 1 * 2³ + 0 * 2² + 0 * 2¹ + 1 * 2⁰ = 16 + 8 + 1 = 25

2. Sketch the signal for 25 in each of the four formats we have discussed: NRZ, RZ, Manchester, and bipolar pulse encoding.
NRZ: 1 is represented by up, 0 represented by down with no transition between bits.

RZ: 1 is represented by an up pulse followed by down, 0 by down.

Manchester: 1 is represented by an up pulse followed by down, 0 by down followed by an up pulse.

bipolar: The quiescent point is a value between up and down. 1 is represented by an up pulse followed by the middle value. 0 is represented by a down pulse followed by the middle value.

3. If your computer can send 10 million amplitudes per second, what bandwidth is needed to transfer your order? What is the bit rate for each of the four formats?
10 million amplitudes per second is equivalent to a pulse rate of 10 MHz. The bandwidth is equal to this pulse rate, so you need 10MHz of bandwidth to send this. In the NRZ format, only a single pulse is required for each bit, thus the bit rate is equal to the pulse rate. In every other format, two amplitudes are required to represent one or both of the binary bits. This gives a bit rate equal to half of the pulse rate, 5 MHz.

1.	What is the binary code for 25? 11001, since 1 2⁴ + 1 * 2³ + 0 * 2² + 0 * 2¹ + 1 * 2⁰ = 16 + 8 + 1 = 25*
2.	Sketch the signal for 25 in each of the four formats we have discussed: NRZ, RZ, Manchester, and bipolar pulse encoding. NRZ: 1 is represented by up, 0 represented by down with no transition between bits. RZ: 1 is represented by an up pulse followed by down, 0 by down. Manchester: 1 is represented by an up pulse followed by down, 0 by down followed by an up pulse. bipolar: The quiescent point is a value between up and down. 1 is represented by an up pulse followed by the middle value. 0 is represented by a down pulse followed by the middle value.
3.	If your computer can send 10 million amplitudes per second, what bandwidth is needed to transfer your order? What is the bit rate for each of the four formats? 10 million amplitudes per second is equivalent to a pulse rate of 10 MHz. The bandwidth is equal to this pulse rate, so you need 10MHz of bandwidth to send this. In the NRZ format, only a single pulse is required for each bit, thus the bit rate is equal to the pulse rate. In every other format, two amplitudes are required to represent one or both of the binary bits. This gives a bit rate equal to half of the pulse rate, 5 MHz.