The effect of signal digitisation in CMB experiments

¹ INAF/Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34131, Trieste, Italy
² Dipartimento di Fisica, Università degli Studi di Milano, Via Celoria 16, 20131, Milano, Italy
³ IASF/CNR, Sezione di Bologna, Via Gobetti 101, 40129, Bologna, Italy
⁴ IASF/CNR, Sezione di Milano, Via Bassini 15, 20131, Milano, Italy

Corresponding author: M. Maris, maris@ts.astro.it

Received: 2 April 2003
Accepted: 15 September 2003

Abstract

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 , with deviations from normality becoming relevant for a relatively small number of repeated measures . At map level, the data quantization alters the noise distribution and the expectation of some higher order moments. We find a constant ratio, , between the RMS of the quantization noise and RMS of the instrumental noise, σ over the map (0.14 for ),
while, for , 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, , that, although related to the instrument and mission parameters, is weakly dependent on the multipole at middle and large and can be quite accurately subtracted. For , the residual uncertainty, , implied by this subtraction is only 1–2% of the RMS uncertainty, , on reconstruction due to the noise power, . Only for the quantization removal is less accurate; in fact, the noise features, although efficiently removed, increase , , and then ; anyway, at low multipoles . This work is based on Planck LFI activities.