Signal-to-quantization-noise ratio (SQNR or SNqR) is widely used quality measure in analysing digitizing schemes such as pulse-code modulation (PCM).
The SQNR reflects the relationship between the maximum nominal signal strength and the quantization error (also known as quantization noise) introduced in the analog-to-digital conversion.
The SQNR formula is derived from the general signal-to-noise ratio (SNR) formula: where: As SQNR applies to quantized signals, the formulae for SQNR refer to discrete-time digital signals.
quantization steps, each sample,
The probability distribution function (PDF) represents the distribution of values in
The maximum magnitude value of any
As SQNR, like SNR, is a ratio of signal power to some noise power, it can be calculated as: The signal power is: The quantization noise power can be expressed as: Giving: When the SQNR is desired in terms of decibels (dB), a useful approximation to SQNR is: where
is the number of bits in a quantized sample, and
is the signal power calculated above.
Note that for each bit added to a sample, the SQNR goes up by approximately 6 dB (