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# Homework 7

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• Chapter 2 in the Anderson text

## Problems

1. Suppose you wish to transmit bits per second over a channel with one-sided bandwidth Hertz.
1. What is the maximum symbol rate that avoids ISI?
2. What is the fewest number of bits per symbol that avoids ISI? Let this number be denoted min.
3. Design a raised-cosine (RC) pulse that occupies the full channel bandwidth. What is the excess bandwidth when there are min bits per symbol?
4. Design a raised-cosine (RC) pulse that occupies the full channel bandwidth. What is the excess bandwidth when there are min bits per symbol?
5. Design a raised-cosine (RC) pulse that occupies the full channel bandwidth. What is the excess bandwidth when there are min bits per symbol?
6. Show graphically (via a sketch in the frequency domain) that the min case avoids ISI.

2. Using a RC pulse to transmit bits/second with bits/symbol, what is the minimum channel bandwidth needed for zero ISI in the samples taken by the sampling receiver?

3. Let the transmitter pulse be given by

Suppose that the symbol set is . Sketch the eye diagram. Be sure to show all possible transitions between symbols.

4. Let the transmitter pulse be given by

Suppose that the symbol set is . Sketch the eye diagram. Be sure to show all possible transitions.

5. Prove that the NRZ pulse defined by

is a Nyquist and a root-Nyquist pulse. Do this in the time domain.
6. Prove that the sinc pulse defined by

 sinc

is a Nyquist pulse and a root-Nyquist pulse. Do this in the frequency domain.
Copyright 2008, by the Contributing Authors. Cite/attribute Resource . admin. (2006, June 29). Homework 7. Retrieved January 07, 2011, from Free Online Course Materials — USU OpenCourseWare Web site: http://ocw.usu.edu/Electrical_and_Computer_Engineering/Communication_Systems_I_1/hw7.html. This work is licensed under a Creative Commons License