MATH233 unit 4 Individual Project

Dr. Claude Shannon (1916 – 2001), “the father of information theory,” observed that the maximum error-free capacity in bits per second (bps) obtainable in a communication channel can be found by the Shannon-Hartley equation:

Above, , is the bandwidth of the channel in Hertz and is the signal-to-noise ratio of the channel. Since 0 does not make sense in this situation, assume that the formula below is correct:

Be sure to show your work details for all calculations and explain in detail how the answers were determined for critical thinking questions. Round all value answers to three decimals.

In the table below, based on the first letter of your last name, choose a bandwidth for your communication channel. Write your maximum error-free channel capacity function.

Calculate the derivative of your channel capacity function with respect to Interpret the meaning of it in terms of channel capacity.

Generate a graph of this function using Excel or another graphing utility. (There are free downloadable programs like Graph 4.4.2 or Mathematics 4.0; or, there are also online utilities such as this site and many others.) Insert the graph into the Word document containing your answers and work details. Be sure to label and number the axes appropriately.

For your function what is the instantaneous rate of change in maximum error-free channel capacity with respect to SNR, for ?

What is the equation of the tangent line to the graph of , when ?

Research the Internet or Library to find a reasonable (signal and noise values should both be in watts) and bandwidth in Hertz for a CAT6 coaxial cable. Be sure to list creditable sources for your research. Based on your research, what would be the theoretical channel capacity for the CAT6 cable’s value that you found?