Quantization and Sampling in Non-Recursive Digital Filtering and in Digital Correlation

摘要

Based on efficient calculation of the mean and standard deviation of inner products of vectors with quantized components, results are presented which are pertinent to estimation of mean values from roughly quantized data and to loss of signal detectability in digital correlation detection. A mean value can be estimated from roughly quantized samples as long as it remains within the quantizer amplitude window and the signal-to-noise ratio is small. The mean-square error for this quantized estimate can be less than the error for an unquantized estimate. Signal detectability in replica correlation is degraded by coarse quantization; and, although the quantizing loss is often large (6 to 10 db) for signal-to-noise ratios greater than one, the signal remains detectable. Much of the loss in signal detectability due to coarse quantization can be regained through faster sampling. (Author)