The effect of signal digitisation in CMB experiments

Abstract

Signal digitisation may produce significant effects in balloon borne or space CMB experiments, when the limited bandwidth for downlink of data requires for loss-less data compression. In fact, the data compressibilty depends on the quantisation 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/ √ 12Ns, 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/( √ 12σ/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, C l , 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, ∆C l , implied by this subtraction is of only ≃1–2% of the RMS uncertainty, ∆C l , on C l reconstruction due to the noise power, C l . Only for l ∼30 the quantization removal is less accurate; in fact, the 1/f noise features, although efficiently removed, increase C l , ∆C noise l , C ex l and then ∆C ex l ; anyway, at low multipoles C sky l ≫ ∆C l > ∆C l . This work is based on Planck LFI activities.

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Cite this paper

@inproceedings{Maris2003TheEO, title={The effect of signal digitisation in CMB experiments}, author={M. Maris}, year={2003} }