quantizer, the dead-zone width can be set to any value by using the forward quantization rule , where the function is the sign function (also known as the signum function). The general reconstruction rule for such a dead-zone quantizer is given by , where is a reconstruction offset value in the range of 0 to 1 as a fraction of the step size. Ordinarily, when quantizing input data with a typical probability density function (PDF) that is symmetric around zero and reaches its peak value at zero (such as a Gaussian, Laplacian, or generalized Gaussian PDF). Although may depend on in general, and can be chosen to fulfill the optimality condition described below, it is often simply set to a constant, such as . (Note that in this definition, due to the definition of the function, so has no effect.) A very commonly used special case (e.g., the scheme typically used in financial accounting and elementary mathematics) is to set and for all . In this case, the dead-zone quantizer is also a uniform quantizer, since the central dead-zone of this quantizer has the same width as all of its other steps, and all of its reconstruction values are equally spaced as well. Noise and error characteristics Additive noise model 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 PDFs. Additive noise behavior is not always a valid assumption. Quantization error (for quantizers defined as described here) is deterministically related to the signal and not entirely independent of it. Thus, periodic signals can create periodic quantization noise. 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. Quantization error models In the typical case, the