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.
- 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.
- 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.
- 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.
- 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?
- What signal-to-noise ratio is needed to put a 1.544 Mbps signal on a
50-kHz line?
- How much bandwidth is there in 0.2 microns of spectrum
at a wavelength of 2 microns? (Answer in Hz.)
- 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?
- Chapter 2, number 11
- Chapter 2, number 15
- What percent overhead is there in the T1 carrier described on page 122?
That is, what percentage of the bits do not contain data?