As SQNR applies to quantized signals, the formulae for SQNR refer to discrete-timedigital signals. Instead of , the digitized signal will be used. For quantization steps, each sample, requires bits. The probability distribution function (PDF) represents 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:
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 ().
References
B. P. Lathi, Modern Digital and Analog Communication Systems (3rd edition), Oxford University Press, 1998