Nyquist Shannon Sampling Theorem easy explanation

Nyquist Sampling Theorem

Nyquist derived an expression for the maximum data rate of a noiseless channel having a finite bandwidth. Nyquist proved that any signal can be reconstructed from its discrete form if the sampling is below the maximum data rate for the channel.

Maximum Data rate= 2H log₂N bits/sec
Where H = Bandwidth of the channel
N= Number of levels in the quantized sample.

Shannon Sampling Theorem

We have already known that the data rate is limited even in the case of the noiseless channel. Random noise is always present in a channel. The channel may again be characterized by the ratio of the signal power to noise power which is known as the Signal-to-Noise Ratio (SNR). It is represented as :

SNR= 10log₁₀(S/N)dB

Shanon derived that in the case of a noisy channel, the signal can be reconstructed from its discrete form if the data rate is below the maximum data rate.

Maximum data rate= Hlog₂(1+S/N) bits/sec
Where H = Bandwidth of the channel and S/N = Signal-to-Noise Ratio