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Signal-to-quantization-noise ratio is widely used quality measure in analysing digitizing schemes such as pulse-code modulation. The SQNR reflects the relationship between the maximum nominal signal strength and the quantization error introduced in the analog-to-digital conversion.
The SQNR formula is derived from the general signal-to-noise ratio formula:
where:
As SQNR applies to quantized signals, the formulae for SQNR refer to discrete-time digital signals. Instead of m {\displaystyle m} , the digitized signal x {\displaystyle x} will be used. For N {\displaystyle N} quantization steps, each sample, x {\displaystyle x} requires ν = log 2 N {\displaystyle \nu =\log _{2}N} bits. The probability distribution function representing the distribution of values in x {\displaystyle x} and can be denoted as f {\displaystyle f}. The maximum magnitude value of any x {\displaystyle x} is denoted by x m a x {\displaystyle x_{max}}.