Briefly explain the Nyquist Bandwidth and Shanon capacity formula

Channel capacity: The maximum rate, at which data can be transmitted over a given communication path or channel under given conditions is referred to as the channel capacity.

There are four concepts that related with channel capacity. They are-

(i) Data rate

(ii) Bandwidth

(iii) Noise

(iv) Error rate

(i) Data rate: This is the rate, in bits per second (bps), at which data can be communicated.

(ii) Bandwidth: This is the bandwidth of the transmitted signal as constrained by the transmitter and by the nature of the transmission medium. It can be expressed as cycles per second or Hertz (Hz).

(iii) Noise: The average level of noise over the communications path.

(iv) Error rate: The rate at which error occur, where an error is the reception of 1 when a 0 was transmitted, or the reception of a 0 when 1 was transmitted.

Nyquist Bandwidth Formula: It the channel is noise free, the limitation of data rate is simply the bandwidth of a signal. A formulation of this limitation due to Nyquist states that,

“if the rate of signal transmission is 2B, then a signal with frequencies no greater than B is sufficient to carry the signal rate.

The converse is also true: Given a bandwidth of B, the highest signal rate that can be carried is 2B.”

With multilevel signaling, the NyQuist formulation becomes,

           

Here,

M = number of discrete signal

C = Channel capacity

B = Bandwidth of channel

Shanon capacity formula: Shanon formula indicates that the maximum channel capacity in bits per second obeys an equation that is, 

           

Here,

C = Capacity of the channel

B = Bandwidth of the channel

SNR = Signal-to-noise ratio

Where this equation is often reported in decibels

   

The signal-to-noise ratio is important in the transmission of digital data.

In other words, the formula defines a characteristic of the channel, not the method of transmission.