The effect of signal digitisation in CMB experiments

Signal digitisation may produce significant effects in balloon - borne or space CMB experiments, when the limited bandwidth for downlink of data requires loss-less data compression. In fact, the data compressibility depends on the quantization step q applied on board by the instrument acquisition chain. In this paper we present a study of the impact of the quantization error in CMB experiments using, as a working case, simulated data from the PLANCK/LFI 30 and 100 GHz channels. At TOD level, the effect of the quantization can be approximated as a source of nearly normally distributed noise, with RMS similar or equal to q/root12N(s), with deviations from normality becoming relevant for a relatively small number of repeated measures N-s less than or similar to 20. At map level, the data quantization alters the noise distribution and the expectation of some higher order moments. We find a constant ratio, similar or equal to 1/(root12sigma/q), between the RMS of the quantization noise and RMS of the instrumental noise, sigma over the map (similar or equal to0.14 for sigma/q similar or equal to 2), while, for sigma/q similar to 2, the bias on the expectation for higher order moments is comparable to their sampling variances. Finally, we find that the quantization introduces a power excess, C-l(ex), that, although related to the instrument and mission parameters, is weakly dependent on the multipole l at middle and large l and can be quite accurately subtracted. For sigma/q similar or equal to 2, the residual uncertainty, DeltaC(l)(ex), implied by this subtraction is only similar or equal to 1 - 2% of the RMS uncertainty, DeltaC(l)(noise), on C-l(sky) reconstruction due to the noise power, C-l(noise). Only for l less than or similar to 30 the quantization removal is less accurate; in fact, the 1/f noise features, although efficiently removed, increase C-l(noise), DeltaC(l)(noise), C-l(ex) and then DeltaC(l)(ex); anyway, at low multipoles C-l(sky) >> DeltaC(l)(noise) > DeltaC(l)(ex). This work is based on PLANCK LFI activities.