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MATH233 Item 4 Individual Project

Dr. Claude Shannon (1916 – 2001), “the father of counsel scheme,” observed that the utmost error-freecalibre in bits per remedy (bps) obtainable in a despatch instrument can be endow by the Shannon-Hartley equation:

Above, , is the bandwidth of the instrument in Hertz and  is the illustrious-to-noiseratio of the instrument. Gone  0 does not constitute significance in this standing, pretend that the formulaunder is correct:

This is a “pure” sum after a while no item addresss on it.The compute of is designated Shannon’s Calibre Limitor instrument calibre. This is the speculative better name for the bits per remedy through the instrument after a while a favoring compute and a favoring dedicated instrument abundance, .

Be indispuconsultation to exhibition your composition specialtys for all calculations and clear-up in specialty how the answers were decided for censorious thinking questions. Round all compute answers to three decimals.

1.      In the consultation under, grounded on the original message of your lastname, select a bandwidth for your despatch instrument.Write your utmost error-unreserved instrument calibre discharge.

(Note: The developed compute of  will be your chosen compute times 1,000,000 gone the consultation computes are in MegaHertz (MHz).)

First message of your lastname

Possible computes for  in MHz

A–F

100199

G–L

200299

M–R

300399

S–Z

400–499

 

2.      Calculate the derivative of your instrument calibre discharge after a while honor to  Interpret the significance of it in conditions of instrument calibre.

 

3.      Generate a graph of this discharge using Excel or another graphing profit. (There are unreserved downloadable programs love Graph 4.4.2 or Mathematics 4.0; or, there are besides onoutline utilities such as this site and frequent others.) Insert the graph into the Word instrument containing your answers and composition specialtys. Be indispuconsultation to address and sum the axes unexceptionably.

 

4.      For your discharge what is the immediate rate of transmute inutmost error-unreserved instrument calibre after a while honor to SNR, for?

 

5.      What is the equation of the tangent outoutline to the graph of , when ?

 

6.      Research the Internet or Library to discover a self-possessed (illustrious and uproar computes should twain be in watts) and bandwidth in Hertz for a CAT6 coaxial cable. Be indispuconsultation to inventory crediconsultation sources for your discovery. Grounded on your discovery, what would be the speculative instrument calibre for the CAT6 cable’s computethat you endow?

 

7.      At what compute of  will

(Note:You cannot rereunfold this equation algebraically using humdrum techniques. Youwill insufficiency to use an equation resolver love Mathematics 4.0 and the deed that  or  by the Change-of-Base formula for logarithms. Or, you may rereunfold this equation by graphing twain  and  on the similar graph to see where these graphs intertwine. Alternatively, you may defy the Lambert W-Function. These are some examples of how you can closely rereunfold equations when the breach cannot be endow abundantly after a while accustomed algebraicmethods.)

References

Desmos. (n.d.). Retrieved from https://www.desmos.com/

Graph 4.4.2. (n.d.). Retrieved from the Graph Web site: http://www.padowan.dk/

Mathematics 4.0. (n.d.). Retrieved from the Microsoft Web site: http://microsoft-mathematics.en.uptodown.com/