## CS601 Assignment No. 4 solution

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 5000×4.7 = 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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