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Quantization Noise Most engineers seem to be conveniently using the 6db per bit formula. As much as it is close to reality most of the time, one must know the assumptions behind the formula to be safe. An engineer should not be using a formula unless he can prove it himself. You may find the theory online easily and please go through it at least once before reading this article. Here I wanted to give an organized summary of Quantization SNR formula with the assumptions made extracting it. The maximum quantization error is constant, and its value expressed in dB relative to 0 dB FS is: e = 20 * log (1 / 2^n) BW: signal frequency fs: Sampling frequency Assumption: Signal occupies the full bit range.
BWSignalRMS valueSNRrmsSNRpeak
fs/2Uniform1/26n+4.77+20log(1/2)+0 = 6n-1.25+06n+4.77+0+0 = 6n+4.77
fs/2Sinus1/root26n+4.77+20log(1/root2)+0 = 6n+1.766n+4.77+0+0 = 6n+4.77
Floating Point SNr: n bits fp: n-m bits mantissa, m bits exponantial DRdb = 6.02 2^m SNRdb = 6.02 (n-m)
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