Question

What is the theoretical capacity of a channel in each of the following cases: i)Bandwidth: 20 KHz SNRdB =40 ii)Bandwidth: 200 KHz SNR =4000 iii) Bandwidth: 1 MHz SNRdB =20​

Answer 1

Answer:

Noiseless Channel : Nyquist Bit Rate –

For a noiseless channel, the Nyquist bit rate formula defines the theoretical maximum bit rate

BitRate = 2 * Bandwidth * log2(L)

In the above equation, bandwidth is the bandwidth of the channel, L is the number of signal levels used to represent data, and BitRate is the bit rate in bits per second.

Bandwidth is a fixed quantity, so it cannot be changed. Hence, the data rate is directly proportional to the number of signal levels.

Note –Increasing the levels of a signal may reduce the reliability of the system.

Examples:

Input1 : Consider a noiseless channel with a bandwidth of 3000 Hz transmitting a signal with two signal levels. What can be the maximum bit rate?

Output1 : BitRate = 2 * 3000 * log2(2) = 6000bps

Input2 : We need to send 265 kbps over a noiseless channel with a bandwidth of 20 kHz. How many signal levels do we need?

Output2 : 265000 = 2 * 20000 * log2(L)

log2(L) = 6.625

L = 26.625 = 98.7 levels