How to quantize noise and calculate signal to noise ratio

Howto quantize and calculate the signal to noise ratio for analog and digital signals

=Terminology=
 * RMS - Root mean squared
 * SNR - Signal to noise ratio
 * ENOB - Effective number of bits
 * dB - decibel
 * Bandwidth

RMS Noise = (Noise level in X/root Hz)*sqrt (bandwidth) $$RMS = \frac{Noise Level}{\sqrt[1]{Hz}}\sqrt[1]{Bandwidth}$$

$$|\bar{z}| = |z|, |(\bar{z})^n| = |z|^n, \arg(z^n) = n \arg(z)\,$$

Dynamic Range = SNR = RMS Full-scale/RMS Noise

Dynamic Range (dB) = SNR (dB) = 20*Log10 (RMS Full-scale/RMS Noise)

ENOB = log (FSR/RMS noise)/log (2)

The relationship between ENOB and SNR is

ENOB = (SNR(in dB) - 1.76) / 6.02