SignaltoQuantizationNoise

Signal-to-quantization-noise ratio (SQNR) is a measure of the fidelity of a digitally represented or processed signal. It compares the average power of the desired signal to the average power of the quantization error introduced when an analog signal is converted to a discrete set of levels by an analog-to-digital converter (ADC) or processed by a digital-to-analog converter (DAC). In practice, SQNR is usually expressed in decibels (dB).

In an ideal N-bit ADC with a full-scale sinusoidal input, the SQNR is approximately 6.02N + 1.76 dB. This result assumes the quantization error behaves as white noise with variance Δ^2/12, where Δ is the quantization step, and that the signal has full-scale amplitude. Practically, this yields about 50 dB for 8 bits and about 98 dB for 16 bits. Real-world SQNR can vary with input amplitude, waveform, and implementation nonidealities.

SQNR depends on the input signal characteristics. If the signal does not utilize the full dynamic range or is not sinusoidal, the actual SQNR can be lower or higher than the ideal estimate. Techniques such as dithering can reduce correlation between quantization error and the signal, effectively improving perceived SQNR. Oversampling and noise shaping, as used in sigma-delta converters, can push quantization noise out of the signal band to improve in-band SQNR.

In applications such as audio, instrumentation, and communications, SQNR serves as a key specification for assessing quantization performance and required bit depth to achieve a target distortion level.