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. Instead of m(t), the digitized signal x(n) will be used. For N quantization steps, each sample, x requires bits. The probability distribution function (PDF) represents the distribution of values in x and can be denoted as f(x). The maximum magnitude value of any x is denoted by x_{max}. 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 \nu is the number of bits in a quantized sample, and P_{x^\nu} is the signal power calculated above. Note that for each bit added to a sample, the SQNR goes up by approximately 6 dB.