MATH233 Item 4 Individual Project
NAME (Required): _____________________________
Dr. Claude Shannon (1916 – 2001), “the father of notification doctrine,” observed that the utmost error-generous compatability in bits per promote (bps) obtainable in a message implement can be base by the Shannon-Hartley equation:
bits per promote
Above, , is the bandwidth of the implement in Hertz and is the signal-to-noise pertinency of the implement. Since 0 does not fashion appreciation in this footing, usurp that the formula underneath is correct:
This is a “pure” calculate delay no item marks on it. The appraise of is denominated Shannon’s Compatability Article or implement compatability. This is the speculative preferable article for the bits per promote through the implement delay a unfair appraise and a unfair dedicated implement quantity bandwidth, , in Hz.
Be infallible to pomp your effect elements for all calculations and elucidate in element how the replys were fixed for momentous thinking doubts. Round all appraise replys to three decimals.
1. In this assignment you get use the subjoined rendering of the Shannon-Hartley equation.
bits per promote
In the board underneath, established on the primitive message of your decisive call, appropriate a appraise from the recurrent stroll for the bandwidth, , for your message implement’s bandwidth. For model, if your decisive call begins delay A-F, and you appropriate 100,000,000 for your appraise of B, then your implement compatability administration for this assignment would be:
bits per promote
Write your utmost error-generous implement compatability administration underneath the board..
First message of your decisive call
Possible appraises for in Hz
A–F
100,000,000 – 125,000,000
G–L
150,000,000 – 175,000,000
M–R
200,000,000 – 225,000,000
S–Z
250,000,000 – 275,000,000
State your implement compatability administration here:
2. Calculate the derivative of your implement compatability administration delay deference to What is the sense of in the matter of this implement compatability scenario? Pomp your effect elements.
3. Genereprove a graph of this administration using Excel or another graphing usefulness. (There are generous downloadable programs approve Graph 4.4.2 or Mathematics 4.0; or, there are as-well ondirection utilities such as this locality and divers others.) Insert the graph into the Word muniment containing your replys and effect elements. Be infallible to mark and calculate the axes uprightly.
4. For your administration from doubt #1 what is the momentary reprove of fluctuate in utmost error-generous implement compatability delay deference to SNR, for ? Pomp your effect elements.
5. What is the equation of the tangent direction to the graph of , when ? Pomp your effect elements.
6. In open, the Shannon-Hartley equation applies to any message implement delay a notorious bandwidth. For model, a plan approve a cable modem may accept a very eminent SNR (> 1000) but a fairly close bandwidth. The Data Over Cable Utility Interface Specification (DOCSIS 3.0) requires that the downstream per implement bandwidth of a handy cable modem must be either 6 MHz or 8 MHz expanded. Research the Library or the Internet to furnish a abstemious downstream bandwidth in MHz of a commercially helpful mark of cable modem. State the call of the commercially helpful cable modem you base and confer the intimation where your base the cable modem notification. Use that bandwidth simultaneously delay an SNR = 1023 to furnish the implement compatability of the cable modem. Whether you accept cable Internet utility or not, are you getting this cast of downstream utility from your Internet Utility Provider? What vindication do you confer for this reply? Pomp your effect elements on all calculations.