Given below are two statements:
Statement $I$: The laws of nature put two fundamental limits on data rate of a channel. The H.Nyquist limit restricts the number of independent samples per second to twice the band-width in a Noiseless channel
Statement $II$: Shannon’s major result about noised channel is that maximum data rate of a channel whose band width is $H$ Hz, and whose signal-to-noise ratio is $S/N$ is given by: Maximum number of bits/sec$=H \log _2 ( 1 + \dfrac{S}{N})$
In the light of the above statements, choose the correct answer from the options given below
- Both Statement $I$ and Statement $II$ are true
- Both Statement $I$ and Statement $II$ are false
- Statement $I$ is correct but Statement $II$ is false
- Statement $I$ is incorrect but Statement $II$ is true