MATH 233 Unit 4 Individual Project
I need help completing this worksheet. I have a value of 225 that must represent B when inserted into the function. All answers must be original! Thank you for your time…..!!! This is a survey of Calculus class for American InterContinental University. The University uses an originality score indicator when an assignment is submitted by a student.
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:
C ( SNR )=B log 2( 1+ SNR )
Above, B , is the bandwidth of the channel in Hertz and SNR is the signal-to-noise ratio of
the channel. Since SNR ≤ 0 does not make sense in this situation, assume that the formula
below is correct:
SNR= Signal Strength∈watts
Noise Strength∈watts This is a “pure” number with no unit labels on it. The value of C(SNR ) is called Shannon’s
Capacity Limit or channel capacity. This is the theoretical upper limit for the bits per second
through the channel with a specific SNR value and a specific given channel frequency, B .
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.
1. 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.
(Note: The actual value of B will be your chosen value times 1,000,000 since the table values are in MegaHertz (MHz).) First letter of your last name Possible values for B in MHz A–F 100 −¿ 199 G–L 200 −¿ 299 M–R 300 −¿ 399
Page 1 of 3 S–Z 400–499 Heath, David – value for B in MHz = 225
2. Calculate C ‘ ( SNR ) , the derivative of your channel capacity function with respect to
SNR . Interpret the meaning of it in terms of channel capacity. 3. Generate a graph of this function C ( SNR ) 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. 4. For your function what is the instantaneous rate of change in maximum error-free channel
capacity with respect to SNR, for SNR =30 ? 5. What is the equation of the tangent line to the graph of C ( SNR ) , when SNR =30 ? 6. Research the Internet or Library to find a reasonable SNR (signal and noise values should both be in watts) and bandwidth in Hertz for a CAT6 Ethernet 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? NOTE: The
conversion formula for converting S/N in decibels to SNR, a pure number as is
required in the Shannon-Hartley equation is: SNR = 10^(dB/10). For example, if the
cable has an S/N of 20 dB, then SNR = 10^(20/10) = 100 as a pure number SNR
value. 7. At what value of SNR ‘
will C ( SNR )=C ( SNR ) ? Page 2 of 3 (Note: You cannot solve this equation algebraically using ordinary techniques. You will need