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 \simeq q / \sqrt { 12 N _ { \mathrm { s } } } , with deviations from normality becoming relevant for a relatively small number of repeated measures N _ { \mathrm { s } } \mbox { $ \stackrel { { } _ { < } } { { } _ { \sim } } $ } 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 } ^ { 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 } ^ { ex } , implied by this subtraction is of only \simeq 1–2 \% of the RMS uncertainty , \Delta C _ { \ell } ^ { noise } , on C _ { \ell } ^ { sky } reconstruction due to the noise power , C _ { \ell } ^ { noise } .
Only for \ell \mbox { $ \stackrel { { } _ { < } } { { } _ { \sim } } $ } 30 the quantization removal is less accurate ; in fact , the 1 / f noise features , although efficiently removed , increase C _ { \ell } ^ { noise } , \Delta C _ { \ell } ^ { noise } , C _ { \ell } ^ { ex } and then \Delta C _ { \ell } ^ { ex } ; anyway , at low multipoles C _ { \ell } ^ { sky } \gg \Delta C _ { \ell } ^ { noise } > \Delta C _ { \ell } ^ { ex } .
This work is based on Planck LFI activities .