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 ≃ q/\sqrt{12 Ns}, with deviations from normality becoming relevant for a relatively small number of repeated measures Ns < 20. At map level, the data quantization alters the noise distribution and the expectation of some higher order moments. We find a constant ratio, ≃ 1/({\sqrt{12}σ/q}), between the RMS of the quantization noise and RMS of the instrumental noise, σ over the map (≃ 0.14 for σ/q ≃ 2), while, for σ/q ˜ 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, Cℓex, 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 σ/q ≃ 2, the residual uncertainty, Δ Cℓex, implied by this subtraction is only ≃1-2% of the RMS uncertainty, Δ Cℓnoise, on Cℓsky reconstruction due to the noise power, Cℓnoise. Only for ℓ ⪉ 30 the quantization removal is less accurate; in fact, the 1/f noise features, although efficiently removed, increase Cℓnoise, Δ Cℓnoise, Cℓex and then Δ Cℓex; anyway, at low multipoles Cℓsky >> Δ Cℓnoise > Δ Cℓex. This work is based on PLANCK LFI activities.