Maximum-Data-Rate-of-Channel

• Maximum Data Rate of a Channel - In 1924, H.Nyquist realized the existence of the fundamental limit and derived the equation expressing the maximum data for a finite bandwidth noiseless channel. In 1948, Claude Shannon carried Nyquist work further and extended it to the case of a channel subject to random noise.

In communications, it is not really the amount of noise that concerns us, but rather the amount of noise compared to the level of the desired signal. That is, it is the ratio of signal to noise power that is important, rather than the noise power alone. This Signal-to-Noise Ratio (SNR), usually expressed in decibel (db), is one of the most important specifications of any communication system. The decibel is the logarithmic unit used for comparisons of power levels or voltage levels. In order to understand the implication of db, it is important to know that a sound level of zero db corresponds to the threshold of hearing, which is the smallest sound that can be heard. A normal speech conversation would measure about 60 db.

If an arbitrary signal is passed through the Low pass filter of bandwidth H, the filtered signal can be completely reconstructed by making only 2H samples per second. Sampling the line faster than 2H per second is pointless. If the signal consists of V discrete levels, then Nyquist theorem states that, for a noiseless channel Maximum data rate= 2H.log2 (V) bits per second.