Q.An amplifier has a SNR of 8 at the input and an SNR of 6 at the output. What are the noise ratio and noise figure?

While the signal-to-noise ratio describes signal quality at one point, the noise ratio (NR) describes how much a system degrades that quality as the signal passes through it. It is defined as the SNR at the input divided by the SNR at the output:

If a stage adds no noise of its own, the output SNR equals the input SNR and $NR = 1$ — the ideal, noiseless case. A real stage always generates some noise, so its output SNR is smaller and the noise ratio comes out greater than 1. The larger the noise ratio, the worse the stage is at preserving signal quality.

Because these ratios can span a wide range, the noise ratio is usually expressed on the decibel scale, where it is called the noise figure (NF):

An ideal system has $NR = 1$ and hence $NF = 0$ dB; a quieter (better) stage has a smaller noise figure. The relation can be inverted to recover the plain noise ratio from a stated noise figure:

These two quantities let engineers put a single number on the noise performance of amplifiers and receivers, and to compare competing designs directly.