Signal-to-Quantization-Noise Ratio (SQNR or SNqR) is widely used quality measure in analysing digitizing schemes such as PCM (pulse code modulation) and multimedia codecs. 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 SNR (Signal-to-Noise Ratio) formula for the binary pulse-code modulated communication channel:
where
As SQNR applies to quantized signals, the formulae for SQNR refer to discrete-time digital signals. Instead of
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