# CS601 - Assignment No. 4 Solution

## CS601 - Assignment No. 4 Solution

Question # 1
A telephone line normally has bandwidth of 5000 Hz, the signal to noise ratio is usually 25dB.Calculate thecapacity of the channel?

When given a bandwidth and a S/N ratio, you need to use the Shannon equation to determine the capacity of the channel in bits/second. Add 1 to your S/N ratio (25+1=26) and take the base 2 logarithm (Log2 of 26=4.7, that is, 2^4.7 = 26) and then multiply this result by the bandwidth (5000). In this case you'll get a capacity of 5000x4.7 = 23,500 bits/second.

You can solve Q No 1 with the help of this question
We can calculate the theoretical highest bit rate of a regular telephone line. A
telephone line normally has a bandwidth of 3000 Hz (300 Hz to 3300 Hz). The signal-to-noise ratio is usually

3162. For this channel the capacity is calculated as
BitRate = 2 × 3000 × log2 2 = 6000 bps
BitRate = 2 × 3000 × log2 4 = 12,000 bps
Capacity = Bandwidth × log2 (1 + SNR)
C = B log2 (1 + SNR) = B log2 (1 + 0) = B log2 (1) = B × 0 = 0
C = B log2 (1 + SNR) = 3000 log2 (1 + 3162) = 3000 log2 (3163)
C = 3000 × 11.62 = 34,860 bps

Question 2: [10]
Why Digital transmission is preferred over analog transmission justify your answer with solid reasons?

Analog vs. Digital Transmission
Compare at two levels:
1. Data continuous (audio) vs. discrete (text)
2. Signaling continuously varying electromagnetic wave vs. sequence of voltage pulses.
Also Transmission transmit without regard to signal content vs. being concerned with signal content. Dierence in how attenuation is handled, but not focus on this.

Improving digital technology
Data integrity. Repeaters take out cumulative problems in transmission. Can thus transmit longer distances.
Easier to multiplex large channel capacities with digital Easy to apply encryption to digital data
Better integration if all signals are in one form. Can integrate voice, video and digital Data.

Solid Reasons:
1. Analog circuits require appliers, and each ampler adds distortion and noise to t signal.

2. In contrast, digital appliers regenerate an exact signal, eliminating cumulative errors. An incoming (analog) signal is sampled, its value is determined, and the nod then generates a new signal from the bit value; the incoming signal is discarded. With analog circuits, intermediate nodes amplify the incoming signal, noise and al

3. Voice, data, video, etc. can all by carried by digital circuits. What about carrying digital signals over analog circuit? The modem example shows the deputies in carrying digital over analog.
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Solution:

Q#2) Why Digital transmission is preferred over analog transmission justify your answer with solid reasons?
There are a wide variety of analog and digital services in which we can compare these two like in ordinary things analog clock and digital clock we compare these two. But if we are talking about services we will talk about telephone services and the internet services.

Analog Services:
In early days our telephone systems are started with the analog system the subscribers were used the analog services and the analog network is called PSTN (Public Switched Telephone Network) and when we connect the modem to our computers the analog signals are digitized for faster speed. Let’s have a look on this aspect:

1) The speed of this service was low
2) There can be more chances of attenuation
3) There can be occurrence of noise while conversation.
4) The speed of the service depends on the bandwidth if carries.
5) The analog services are not more reliable.

Digital Service:
Nowadays digital services are taking place of analog services because in this IT world every thing is becoming more faster and saying Bye to the slower services.

THESE ARE THE POINTS OF WHICH WE PREFFERED DIGITAL TRANSMISSION:
SPEED:

1) The speed of this service is very high.

SMOOTH PERFORMANCE:

2) There can be less chances of attenuation.

NOISE REDUCTION:

3) There can be less noise

BIT RATES:

4) The speed depends upon the bit rates

RELIABILITY:.

5) The digital services are more reliable
Hence that time is not far away when every service and task will be done digitally.
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