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:
- is the probability of received bit error
- is the peak message signal level
- is the mean message signal level
As SQNR applies to quantized signals, the formulae for SQNR refer to discrete-time digital signals. Instead of , the digitized signal will be used. For quantization steps, each sample, requires bits. The probability distribution function (pdf) representing the distribution of values in and can be denoted as . The maximum magnitude value of any is denoted by .
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:
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 6dB ().
- B. P. Lathi , Modern Digital and Analog Communication Systems (3rd edition), Oxford University Press, 1998
- Signal to quantization noise in quantized sinusoidal - Analysis of quantization error on a sine wave