Amplitude-quantised sample of unknown signal plus noise

The paper considers each of the digitised data obtained by measuring an unknown signal contaminated by noise and afterwards by the quantisation error. The first case considered is that when there is no a priori knbowledge about the amplitude of the signal. A simple equation is derived for the conditional-probability density function of the combined output error, and from this, the signal confidence interval is obtained. The noise may have an arbitrary probability distribution, and the quantisation step may also be arbitrary. Numerical results are presented for Gaussian noise. The standard deviation of both the quantisation error and the output error are also given. The second case considered is that for which there exists some a priori knowledge about the signal amplitude. The conditional probability density function of the output error and the probablities of the quantised outputs are given, the purpose of the latter being to inidicate the extent to which a specific number of quantisation levels is acceptable. These results are applied to the case where there is a known range of magnitude of the signal.