Signal-to-quantization-noise ratio (SQNR or SN
qR) is widely used quality measure in analysing
digitizing
DigitizationTech Target. (2011, April). Definition: digitization. ''WhatIs.com''. Retrieved December 15, 2021, from https://whatis.techtarget.com/definition/digitization is the process of converting information into a digital (i.e. computer- ...
schemes such as
pulse-code modulation
Pulse-code modulation (PCM) is a method used to digitally represent sampled analog signals. It is the standard form of digital audio in computers, compact discs, digital telephony and other digital audio applications. In a PCM stream, the ...
(PCM). The SQNR reflects the relationship between the maximum nominal
signal strength
In telecommunications, particularly in radio frequency engineering, signal strength refers to the transmitter power output as received by a reference antenna at a distance from the transmitting antenna. High-powered transmissions, such as those u ...
and the
quantization error
Quantization, in mathematics and digital signal processing, is the process of mapping input values from a large set (often a continuous set) to output values in a (countable) smaller set, often with a finite number of elements. Rounding and ...
(also known as quantization noise) introduced in the
analog-to-digital conversion.
The SQNR formula is derived from the general
signal-to-noise ratio
Signal-to-noise ratio (SNR or S/N) is a measure used in science and engineering that compares the level of a desired signal to the level of background noise. SNR is defined as the ratio of signal power to the noise power, often expressed in de ...
(SNR) formula:
:
where:
:
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:
:
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 6dB (
).
References
* B. P. Lathi , Modern Digital and Analog Communication Systems (3rd edition), Oxford University Press, 1998
External links
Signal to quantization noise in quantized sinusoidal- Analysis of quantization error on a sine wave
{{Noise
Digital audio
Engineering ratios
Noise (electronics)