3. A channel, whoseanidth is 3 MHk, has an intenled capacily o20 M, Assing whie

Question

3. A channel, whoseanidth is 3 MHk, has an intenled capacily o20 M, Assing whie thernal noisc, what signal to noise ratio is rcquircd to achicvc this capacity? 4. Supposc that data is storcd on 14 Mbyte floppy diskcttcs that weight 3o g cach. Supposc that an airliner came 10 4 Kg if I hese fleppies al a speed of 1000 Krn h over a dislälice r'500 ) Kill. Whal is lhe dala transmission rate in bps of this system? 5. Arc the modcm and codec functional inverscs (i.c., could an invcrted modem function as a codec. or vice versa 6. Is an oil pipelirne simplex, half duplex, or full duplex?

Explanation / Answer

3. From Shannon's formula (because white thermal noise is assumed) :

capacity = bandwidth * logbase2 (1 + SNR)
20 Mbps = 3 MHz * logbase2 (1 + SNR)
20* 10^6 = (3* 10^6) * logbase2 (1 + SNR)
20 / 3 = logbase2 (1 + SNR)
6.667 = logbase2 (1 + SNR)
2^6.667 = (1 + SNR)
101.6 = (1 + SNR)
Hence, SNR = 100.6
This is required signal-to-noise-ratio.

4. Calculate the time for which data was carried

Time=distance/speed

Elapsed time = (5000 km)/(1000 km/hr) = 5 hours = 18,000 seconds

Amount of data per diskette = 1.4 x 220 x 8 = 11.74 x 106 bits/diskette

Now given that weight of each floppy is 30gms and total load carries is 104 kgs=107 gms

Therefore, Number of diskettes or floppy carried = (107 g)/(30 g/diskette) = 333333 diskettes

Now each floppy contains 11.74 x 106 bits

So 333333 floppy contains=333333*11.74 x 106 bits

Data transmission speed= data carried in bits/time

                                    = (333333*11.74 x 106 bits) / (5hrs*60mins*60 sec)

                                    = 217 Mbps (approx.)

5. No, codecs and modems are not functionally inverse. One is used convert analog into digital and the other is used to convert digital to analog, so both of them have different techniques.

6. Oil pipeline will be classifies as simplex because in pipeline oil flows only in one direction, however theoretically it can be considered as half duplex (flow in one direction at a time) but it would be impractical to change the direction of flow.

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