EDP Sciences
Free access
Volume 414, Number 2, February I 2004
Page(s) 777 - 794
Section Physical and chemical processes
DOI http://dx.doi.org/10.1051/0004-6361:20031489

A&A 414, 777-794 (2004)
DOI: 10.1051/0004-6361:20031489

The effect of signal digitisation in CMB experiments

M. Maris1, D. Maino2, C. Burigana3, A. Mennella4, M. Bersanelli2, 4 and F. Pasian1

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

(Received 2 April 2003 / Accepted 15 September 2003 )

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 $\simeq
q/\sqrt{12 N_{\mathrm{s}}}$ , with deviations from normality becoming relevant for a relatively small number of repeated measures $N_{\mathrm{s}} \la 20$. At map level, the data quantization alters the noise distribution and the expectation of some higher order moments. We find a constant ratio, ${\simeq}
1/({\sqrt{12}\sigma/q})$ , between the RMS of the quantization noise and RMS of the instrumental noise, $\sigma$ over the map ( $\simeq $0.14 for $\sigma/q \simeq 2$),

while, for $\sigma/q \sim 2$, 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, $C_\ell^{\mathrm{ex}}$, that, although related to the instrument and mission parameters, is weakly dependent on the multipole $\ell$ at middle and large $\ell$ and can be quite accurately subtracted. For $\sigma/q \simeq 2$, the residual uncertainty, $\Delta
C_\ell^{\mathrm{ex}}$ , implied by this subtraction is only $\simeq $1-2% of the RMS uncertainty, $\Delta C_\ell^{\mathrm{noise}}$, on $C_\ell^{\mathrm{sky}}$ reconstruction due to the noise power, $C_\ell^{\mathrm{noise}}$. Only for $\ell \la 30$ the quantization removal is less accurate; in fact, the 1/f noise features, although efficiently removed, increase $C_\ell^{\mathrm{noise}}$, $\Delta C_\ell^{\mathrm{noise}}$ , $C_\ell^{\mathrm{ex}}$ and then $\Delta
C_\ell^{\mathrm{ex}}$; anyway, at low multipoles $C_\ell^{\mathrm{sky}} \gg \Delta C_\ell^{\mathrm{noise}} > \Delta C_\ell^{\mathrm{ex}}$. This work is based on PLANCK LFI activities.

Key words: methods: data analysis -- statistical; cosmology: cosmic microwave background

Offprint request: M. Maris, maris@ts.astro.it

© ESO 2004