Signal-to-quantization-noise ratio
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:
- 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) 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
External links
- Signal to quantization noise in quantized sinusoidal - Analysis of quantization error on a sine wave
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terms
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- Noise figure
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- Carrier-to-noise ratio (C/N)
- Carrier-to-receiver noise density (C/kT)
- dBrnC
- Eb/N0 (energy per bit to noise density)
- Es/N0 (energy per symbol to noise density)
- Modulation error ratio (MER)
- Signal, noise and distortion (SINAD)
- Signal-to-interference ratio (S/I)
- Signal-to-noise ratio (S/N, SNR)
- Signal-to-noise ratio (imaging)
- Signal-to-interference-plus-noise ratio (SINR)
- Signal-to-quantization-noise ratio (SQNR)
- Contrast-to-noise ratio (CNR)
- List of noise topics
- Acoustics
- Colors of noise
- Interference (communication)
- Noise generator
- Spectrum analyzer
- Thermal radiation
methods
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