CS 4873 Computer Networks, Fall 1997 Assignment 1

Due Thursday, September 18 at the start of class


Print out the postscript file: /usr/local/courses/cs4873/fall97/cover1.ps and use it as the cover sheet for your assignment.
  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. Your graphs should look something like the ones here. 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/fall97/chapter2/gnufile.

  2. Compute the Fourier coefficients for the functions h(t) and k(t) described below on the interval [0,T]. 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 in some printings of the book the value of c is given as 3/8 instead of 3/4. Modify your program from question 1) to produce graphs similar to those in figure 2.1. They should look something like Also draw a graph showing the sum of the first 64 harmonics. Your graphs should look something like these.

  3. Television signals are 6 MHz wide. How many bits per second can be sent if binary digital signals are used? What signal-to-noise ratio is needed? Answer in dB.

  4. If a 4-level signal is sent over a 3-kHz channel whose signal-to-noise ratio is 30 dB, what is the maximum achievable data rate?

  5. What signal-to-noise ratio is needed to put a 1.544 Mbps signal on a 50-kHz line?

  6. How much bandwidth is there in 0.2 microns of spectrum at a wavelength of 2 microns? (Answer in Hz.)

  7. It is desired to send a sequence of computer screen images over a data line. Assume a screen size of 1024 by 768 and 24 bits per pixel. If 60 screen images must be sent per second, how many bits per second is this?

  8. Chapter 2, number 11

  9. Chapter 2, number 15

  10. What percent overhead is there in the T1 carrier described on page 122? That is, what percentage of the bits do not contain data?