An outline is given of the nature of aliasing errors, which are caused if the signal is not band limited before sampling. In the case of sensors with digital output, bandpass filtering before sampling is often impossible because of the direct coupling with the process to be measured. The errors are treated, leading to exact as well as to approximate results. Several ways of minimizing the errors are considered which take into account the influence of signal processing after sampling and the consequences of non-ideal demodulation filtering (interpolation). The investigations show among other things the new and important result that, in the case of a mean operation, the sampling frequency may only be half the value due to the sampling theorem. Beyond this, the pulse shape of the samples should be chosen in such a way that the spectral density decreases with frequency as fast as possible. A numerical example demonstrates the efficiency of these methods.