Homework on Signal Characterization (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.

Optical fibers carry signals in multiple "channels" simultaneously, with each channel assigned to a specific bandwidth of frequencies. Suppose each channel has a bandwidth of 20 MHz.

1. Optical fibers are particularly useful for long-distance, high-capacity transmission, such as sending phone messages across (under) the ocean. Which data format (NRZ, RZ, Manchester, Bipolar) do you think would be most useful in such a situation? Justify your answer.

Any well-considered response is acceptable.

2. Sketch the signal that represents the binary string 1101001 using the format you specified above.

3. If your 20 MHz bandwidth carries a signal of the format you specified above, at what bitrate can information be sent in that channel?

The NRZ bitrate is equal to the bandwidth: 1 GHz. For the other formats, the bitrate is half of the bandwidth: 500 MHz.

4. At that rate, how long (in time) would the signal be for a 100-page document averaging 1000 letters/page? Assume you use ASCII, with 8 bits for each character.

800,000 bits need to be sent. For NRZ, it takes 1 ns to send one bit, and so 0.8 ms to send the entire document. For the other formats, it takes 2 ns to send one bit, and 1.6 ms to send the whole thing.

5. What is the maximum allowed rise time for a bit in this signal?

The rise and fall times together may be 70% of the width of an amplitude at most. Thus, the maximum acceptable rise time (assuming a fall time of zero) is 0.7 ns.

1.	Optical fibers are particularly useful for long-distance, high-capacity transmission, such as sending phone messages across (under) the ocean. Which data format (NRZ, RZ, Manchester, Bipolar) do you think would be most useful in such a situation? Justify your answer.
	Any well-considered response is acceptable.
2.	Sketch the signal that represents the binary string 1101001 using the format you specified above.

3.	If your 20 MHz bandwidth carries a signal of the format you specified above, at what bitrate can information be sent in that channel?
	The NRZ* bitrate is equal to the bandwidth: 1 GHz. For the other formats, the bitrate is half of the bandwidth: 500 MHz.*
4.	At that rate, how long (in time) would the signal be for a 100-page document averaging 1000 letters/page? Assume you use ASCII, with 8 bits for each character.
	800,000 bits need to be sent. For NRZ, it takes 1 ns to send one bit, and so 0.8 ms to send the entire document. For the other formats, it takes 2 ns to send one bit, and 1.6 ms to send the whole thing.
5.	What is the maximum allowed rise time for a bit in this signal?
	The rise and fall times together may be 70% of the width of an amplitude at most. Thus, the maximum acceptable rise time (assuming a fall time of zero) is 0.7 ns.