Generalized model of the quantization error-a unified approach

The effective resolution of AD converters is a crucial quantization quality parameter in modern instrumentation. A usual theoretical assumption about the quantized (training) signal is that it is a pure sine wave with a "zero" offset. This means that either the average value of the sine wave is equal to one of the threshold levels (quantizer without dead zone) or that it lies exactly in the middle of them (rounding quantizer). In the measurement technique this assumption is hardly fulfilled, and that is why we meet something intermediate between the above-mentioned hypothetical situations. Here we generalize the known results for "zero" offset to the case of unknown offset. A general problem of an arbitrary random offset distribution is considered first. Two important practical cases are then analyzed. The first one is an unknown and nonrandom offset (one-point distribution). The second one is a case of a uniform distribution of the offset (effect of dithering on quantizer input). In particular, the expected values and variances are derived and analyzed versus the offset and the number of quantizing levels. The results obtained are applied to the effective resolution measurement.