Quantization (signal Processing) - The Additive Noise Model For Quantization Error

The Additive Noise Model For Quantization Error

A common assumption for the analysis of quantization error is that it affects a signal processing system in a similar manner to that of additive white noise – having negligible correlation with the signal and an approximately flat power spectral density. The additive noise model is commonly used for the analysis of quantization error effects in digital filtering systems, and it can be very useful in such analysis. It has been shown to be a valid model in cases of high resolution quantization (small relative to the signal strength) with smooth probability density functions. However, additive noise behaviour is not always a valid assumption, and care should be taken to avoid assuming that this model always applies. In actuality, the quantization error (for quantizers defined as described here) is deterministically related to the signal rather than being independent of it, and in some cases it can even cause limit cycles to appear in digital signal processing systems.

One way to ensure effective independence of the quantization error from the source signal is to perform dithered quantization (sometimes with noise shaping), which involves adding random (or pseudo-random) noise to the signal prior to quantization. This can sometimes be beneficial for such purposes as improving the subjective quality of the result, however it can increase the total quantity of error introduced by the quantization process.