SQNR
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The acronym SQNR (standing for Signal-to-Quantization Noise Ratio) is widely used in communication systems analysis, particularly in PCM (pulse code modulation) schemes.
The SQNR formula is derived from the general SNR (Signal-to-Noise Ratio) formula for the binary pulse-code modulated communication channel.
where
Pe is the probability of received bit error
m(t) is the message signal
Since SQNR applies to quantized signals, then the formulae involved with SQNR refer to discrete-time digital signals. Thus, instead of m(t), we will used the digitized signal x(n). For N quantization steps, there are ν = log2N bits needed for each sample, x. The probability distribution function (pdf) representing the distribution of values in x and can be denoted as f(x). The maximum magnitude value of any x is denoted by xmax.
Since SQNR, like SNR, is a ratio of signal power to some noise power, we calculate ![SQNR=\frac{P_{signal}}{P_{noise}}=\frac{E[x^2]}{E[\tilde{x}^2]}](../../../math/c/3/0/c302117c3787d37d92e2be730c0c68d1.png)
The signal power is calculated ![E[x^2]=P_{x^\nu}=\int_{}^{}x^2f(x)dx](../../../math/f/c/b/fcbaafe597bfb781ff83a383872d7885.png)
and will be notated 
. The quantization noise power can be expressed 
This leads to 
When the SQNR is desired in terms of Decibels (dB), a useful approximation to SQNR is as follows: 
where ν 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 about 6dB.
[edit] References
- B.P.Lathi, Modern Digital and Analog Communication Systems (3rd edition), Oxford University Press, 1998
- Gimmy Chu - University Of Toronto, 2005
- Pavel Chtchetinin - University Of Toronto, 2005
[edit] External Links
- Signal to quantization noise in quantized sinusoidal - Analysis of quantization error on a sine wave
