arXiv subjects

S. Siegel

Publications and source records attributed to S. Siegel.

3 recordsLinked to original sources

arXiv2018

Quantization bias for digital correlators

In radio interferometry, the quantization process introduces a bias in the magnitude and phase of the measured correlations which translates into errors in the measurement of source brightness and position in the sky, affecting both the system calibration and image reconstruction. In this paper we investigate the biasing effect of quantization in the measured correlation between complex-valued inputs with a circularly symmetric Gaussian probability density function (PDF), which is the typical case for radio astronomy applications. We start by calculating the correlation between the input and quantization error and its effect on the quantized variance, first in the case of a real-valued quantizer with a zero mean Gaussian input and then in the case of a complex-valued quantizer with a circularly symmetric Gaussian input. We demonstrate that this input-error correlation is always negative for a quantizer with an odd number of levels, while for an even number of levels this correlation is positive in the low signal level regime. In both cases there is an optimal interval for the input signal level for which this input-error correlation is very weak and the model of additive uncorrelated quantization noise provides a very accurate approximation. We determine the conditions under which the magnitude and phase of the measured correlation have negligible bias with respect to the unquantized values: we demonstrate that the magnitude bias is negligible only if both unquantized inputs are optimally quantized (i.e., when the uncorrelated quantization error model is valid), while the phase bias is negligible when 1) at least one of the inputs is optimally quantized, or when 2) the correlation coefficient between the unquantized inputs is small. Finally, we determine the implications of these results for radio interferometry.

astro-ph.IM↗

arXiv2016

ICE: a scalable, low-cost FPGA-based telescope signal processing and networking system

We present an overview of the 'ICE' hardware and software framework that implements large arrays of interconnected FPGA-based data acquisition, signal processing and networking nodes economically. The system was conceived for application to radio, millimeter and sub-millimeter telescope readout systems that have requirements beyond typical off-the-shelf processing systems, such as careful control of interference signals produced by the digital electronics, and clocking of all elements in the system from a single precise observatory-derived oscillator. A new generation of telescopes operating at these frequency bands and designed with a vastly increased emphasis on digital signal processing to support their detector multiplexing technology or high-bandwidth correlators---data rates exceeding a terabyte per second---are becoming common. The ICE system is built around a custom FPGA motherboard that makes use of an Xilinx Kintex-7 FPGA and ARM-based co-processor. The system is specialized for specific applications through software, firmware, and custom mezzanine daughter boards that interface to the FPGA through the industry-standard FMC specifications. For high density applications, the motherboards are packaged in 16-slot crates with ICE backplanes that implement a low-cost passive full-mesh network between the motherboards in a crate, allow high bandwidth interconnection between crates, and enable data offload to a computer cluster. A Python-based control software library automatically detects and operates the hardware in the array. Examples of specific telescope applications of the ICE framework are presented, namely the frequency-multiplexed bolometer readout systems used for the SPT and Simons Array and the digitizer, F-engine, and networking engine for the CHIME and HIRAX radio interferometers.

astro-ph.IM↗

arXiv2015

Galaxy Cluster Scaling Relations between Bolocam Sunyaev-Zel'dovich Effect and Chandra X-ray Measurements

We present scaling relations between the integrated Sunyaev-Zel'dovich Effect (SZE) signal, $Y_{\rm SZ}$, its X-ray analogue, $Y_{\rm X}\equiv M_{\rm gas}T_{\rm X}$, and total mass, $M_{\rm tot}$, for the 45 galaxy clusters in the Bolocam X-ray-SZ (BOXSZ) sample. All parameters are integrated within $r_{2500}$. $Y_{2500}$ values are measured using SZE data collected with Bolocam, operating at 140 GHz at the Caltech Submillimeter Observatory (CSO). The temperature, $T_{\rm X}$, and mass, $M_{\rm gas,2500}$, of the intracluster medium are determined using X-ray data collected with Chandra, and $M_{\rm tot}$ is derived from $M_{\rm gas}$ assuming a constant gas mass fraction. Our analysis accounts for several potential sources of bias, including: selection effects, contamination from radio point sources, and the loss of SZE signal due to noise filtering and beam-smoothing effects. We measure the $Y_{2500}$--$Y_{\rm X}$ scaling to have a power-law index of $0.84\pm0.07$, and a fractional intrinsic scatter in $Y_{2500}$ of $(21\pm7)\%$ at fixed $Y_{\rm X}$, both of which are consistent with previous analyses. We also measure the scaling between $Y_{2500}$ and $M_{2500}$, finding a power-law index of $1.06\pm0.12$ and a fractional intrinsic scatter in $Y_{2500}$ at fixed mass of $(25\pm9)\%$. While recent SZE scaling relations using X-ray mass proxies have found power-law indices consistent with the self-similar prediction of 5/3, our measurement stands apart by differing from the self-similar prediction by approximately 5$σ$. Given the good agreement between the measured $Y_{2500}$--$Y_{\rm X}$ scalings, much of this discrepancy appears to be caused by differences in the calibration of the X-ray mass proxies adopted for each particular analysis.

astro-ph.CO↗