Generalized model of the quantization error and its application to the effective resolution estimation

The effective resolution of analog to digital converters is a crucial quantization quality parameter in modern instrumentation. A usual theoretical assumption about the quantized signal is that this is a pure sine wave with a zero offset. Here, the authors generalize the known results for zero offset to the case of unknown offset. A general problem of an arbitrary random offset distribution is considered. Two important practical cases are then analyzed. The first one is an unknown and nonrandom offset. The second one is a case of an uniform distribution of the offset. In particular, the expected values and variances are derived and analyzed versus the offset and the number of quantizer bits. The results obtained improve the repeatibility of the effective resolution measurement