type of quantizer, and the bit rate range of operation. However, it is common to assume that for many sources, the slope of a quantizer SQNR function can be approximated as 6 dB/bit when operating at a sufficiently high bit rate. At asymptotically high bit rates, cutting the step size in half increases the bit rate by approximately 1 bit per sample (because 1 bit is needed to indicate whether the value is in the left or right half of the prior double-sized interval) and reduces the mean squared error by a factor of 4 (i.e., 6 dB) based on the approximation. At asymptotically high bit rates, the 6 dB/bit approximation is supported for many source PDFs by rigorous theoretical analysis. Moreover, the structure of the optimal scalar quantizer (in the rate–distortion sense) approaches that of a uniform quantizer under these conditions. In other fields Many physical quantities are actually quantized by physical entities. Examples of fields where this limitation applies include electronics (due to electrons), optics (due to photons), biology (due to DNA), physics (due to Planck limits) and chemistry (due to molecules). See also Beta encoder Color quantization Data binning Discretization Discretization error Posterization Pulse-code modulation Quantile Quantization (image processing) Regression dilution – a bias in parameter estimates caused by errors such as quantization in the explanatory or independent variable Notes References Further reading Digital signal processing Computer graphic artifacts Digital audio Noise (electronics) Signal processing Telecommunication theory