CS 4873 Computer Networks, Fall 1996 Assignment 1

• Due Thursday, September 19 at the start of class

1. In class we computed the Fourier coefficients for the function g(t) which was 1 in the interval from 0 to T/8 and zero elsewhere. Assume that T=1. Write a program that outputs a table of values for the sum of the series through the nth harmonic, where n is passed on the command line. Output values of the function for t between 0 and 1 in increments of 0.005. Run your program for n = 1, 4, 8, 16, and 64. Draw a graph for each. There are utilities available on ringer to draw these graphs, gnuplot is one. A sample input file for gnuplot can be found in
   /usr/local/courses/cs4873/fall96/chapter2/gnufile.

2. Compute the Fourier coefficients for the functions h(t) and k(t) described as follows. h(t) is 1 in the interval from T/8 to 3T/8, and zero elsewhere. k(t) in 1 in the interval from 3T/4 to 7T/8 and zero elsewhere. By adding the corresponding coefficients together, you should get the Fourier coefficients for the function shown in figure 2.1. The result is given on page 78 but one of the answers there is incorrect. Modify your program from question 1) to produce graphs similar to those in figure 2.1. Also draw a graph showing the sum of the first 64 harmonics.

3. Chapter 2, number 3
   Also, what signal-to-noise ratio is needed? Answer in dB.

4. Chapter 2, number 4

5. Chapter 2, number 7 (Answer in Hz.)

6. Chapter 2, number 8 (Assume 1 bps per Hz.)

7. Chapter 2, number 11

8. Chapter 2, number 13

9. Chapter 2, number 15

10. Chapter 2, number 20