Question

Why is the maximum data rate of a channel dependent on the channel's cutoff frequency?

Answer 1

• Data rate governs the speed of data transmission. A very important consideration in data communication is how fast we can send data, in bits per second, over a channel. Data rate depends upon 3 factors:
• The bandwidth available
• Number of levels in digital signal
• The quality of the channel – level of noise
• Two theoretical formulas were developed to calculate the data rate: one by Nyquist for a noiseless channel, another by Shannon for a noisy channel.

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.

Noisy Channel : Shannon Capacity –

• In reality, we cannot have a noiseless channel; the channel is always noisy. Shannon capacity is used, to determine the theoretical highest data rate for a noisy channel:

• Capacity = bandwidth * log2(1 + SNR)

• In the above equation, bandwidth is the bandwidth of the channel, SNR is the signal-to-noise ratio, and capacity is the capacity of the channel in bits per second.
• Bandwidth is a fixed quantity, so it cannot be changed. Hence, the channel capacity is directly proportional to the power of the signal, as SNR = (Power of signal) / (power of noise).
• The signal-to-noise ratio (S/N) is usually expressed in decibels (dB) given by the formula:

             10 * log10(S/N)

so for example a signal-to-noise ratio of 1000 is commonly expressed as:

                 10 * log10(1000) = 30 dB.