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