The effect of signal digitisation in CMB experiments

Abstract

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 P/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/ √ 12N s , with deviations from normality becoming relevant for a relatively small number of repeated measures N s < ∼ 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 ex , 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 σ/q 2, the residual uncertainty, ∆C ex , implied by this subtraction is only 1-2% of the RMS uncertainty, ∆C noise , on C sky reconstruction due to the noise power, C noise . Only for < ∼ 30 the quantization removal is less accurate; in fact, the 1/ f noise features, although efficiently removed, increase C noise , ∆C noise , C ex and then ∆C ex ; anyway, at low multipoles C sky ∆C noise > ∆C ex . This work is based on P LFI activities.

Virtually Lossless Compression of Astrophysical Images

“…This protocol is substantially in accordance with the results reported by Maris et al [5]. The main difference is operative.…”

“…In fact, for an astronomer a scientific frame is not simply a scene to be reproduced with a more or less high fidelity, but a 2D measure of a scalar field representing fluxes. Then, as for any other measure, random and systematic errors must be carefully assessed, quantified, and kept under strict control [5]. A common practice to achieve this goal, given the root mean square (RMS) of the noise introduced by the analog instrument, is that the step size of the uniform threshold quantizer (UTQ) is chosen accordingly, based on application requirements; for example, target detection, and the outcome quantization levels are transmitted without further loss.…”

Planckpre-launch status: ThePlanckmission

“…The sky and reference load time-ordered data are then "mixed" to reduce variability due to correlated noise and drifts, and requantised to an equivalent 6 σ/q ∼ 9, leading to a σ/q ∼ 2 for the sky and reference recovered signals. This process adds less than 0.05% extra white noise (see Maris et al 2004 for a description of the effects of quantisation on the noise distribution). Finally, the mixed and re-quantised time-ordered data are recoded using an adaptive lossless algorithm into packets of maximum capacity of 980 bytes equivalent to about 1172 compressed samples.…”

Planckpre-launch status: Low Frequency Instrument calibration and expected scientific performance

“…Previous optimisation studies (Maris et al 2004) demonstrated that a quantisation ratio σ/q ∼ 2 is enough to satisfy telemetry requirements without significantly increasing the noise level. This has been verified during calibration tests using the so-called "calibration channel", i.e., a data channel containing about 15 minutes per day of unquantised data from each detector.…”