pith. machine review for the scientific record. sign in

arxiv: 2605.05489 · v1 · submitted 2026-05-06 · 🌌 astro-ph.IM · astro-ph.CO

Recognition: unknown

Systematic Spectral Distortion from Digital Whitening in Radio Telescopes and Implications for 21 cm Cosmology

Daniel C. Jacobs, Gregg Hallinan, Larry R. D'Addario, Ruby Byrne

Pith reviewed 2026-05-08 15:35 UTC · model grok-4.3

classification 🌌 astro-ph.IM astro-ph.CO
keywords spectral distortiondigital whiteningre-quantizationradio telescopes21 cm cosmologyOVRO-LWAgain calibrationdigital signal processing
0
0 comments X

The pith

Digital whitening of radio signals followed by re-quantization introduces systematic spectral distortions at levels problematic for 21 cm cosmology.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper demonstrates that a standard processing step in wide-bandwidth radio telescopes—flattening the incoming spectrum through digital whitening and then re-quantizing the samples—produces a frequency-dependent error in the measured gain. This occurs because the whitening step allocates bits assuming a flat spectrum, but real signals vary in power across frequency, leaving residual inaccuracies after re-quantization. The resulting distortion is subtle enough to have gone unnoticed until now but reaches amplitudes that bias the faint spectral features targeted by 21 cm cosmology experiments. The authors confirm the effect both in actual data from the OVRO-LWA array and in controlled semi-analytic simulations, while also showing that it can be reduced by adjusting gain distribution or adding dithering before re-quantization.

Core claim

The central claim is that the whitening-plus-re-quantization sequence, routinely used to enable efficient low-bit processing of wideband radio signals, creates a systematic distortion in the telescope's gain-versus-frequency response. This distortion is visible in OVRO-LWA observations and reproduced in simulations; it reaches levels that compromise the spectral precision required for 21 cm cosmology while remaining small enough for most other applications.

What carries the argument

The whitening-plus-re-quantization sequence, which flattens signal power across frequency to fit within a limited number of bits and then re-quantizes the channelized data.

If this is right

  • Precision spectral experiments such as 21 cm cosmology must either correct for or avoid the whitening-induced distortion in their data pipelines.
  • Choosing a different gain distribution along the analog and digital signal path can substantially reduce the size of the distortion.
  • Adding dithering noise before the re-quantization step further suppresses the systematic error.
  • Any telescope using similar wideband digital processing may carry unrecognized spectral artifacts that affect faint-signal science.
  • Calibration strategies that assume a smooth instrumental response will need to incorporate this effect to reach the required accuracy.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same processing sequence could introduce comparable artifacts in other radio-astronomy domains that rely on accurate broad-band spectra, such as fast radio burst studies or spectral-line surveys.
  • Future instrument designs could embed dithering hardware at the re-quantization stage to eliminate the distortion at the source rather than correcting it later.
  • The effect may interact with existing calibration models, suggesting that joint fitting of whitening parameters with other instrumental terms could improve overall data fidelity.

Load-bearing premise

The distortion measured in OVRO-LWA data and simulations is caused specifically by the whitening and re-quantization steps rather than by unrelated instrumental or environmental effects.

What would settle it

High-precision spectral measurements taken with the whitening step deliberately disabled or bypassed, compared directly against the same observations processed through the standard whitening-plus-re-quantization chain, would show whether the distortion disappears.

Figures

Figures reproduced from arXiv: 2605.05489 by Daniel C. Jacobs, Gregg Hallinan, Larry R. D'Addario, Ruby Byrne.

Figure 1
Figure 1. Figure 1: Block diagram of the typical per-signal processing architecture. Blue hexagons denote processing steps and green rectangles denote data and data products. This structure is applicable, with small variations, to many instruments. The signal from an antenna is amplified and filtered in analog circuitry, then sampled at rate fs and quantized to b1 bits. It is then analyzed in a digital filter bank to produce … view at source ↗
Figure 2
Figure 2. Figure 2: Left: Spectrum of one signal from the OVRO-LWA, measured at the output of the filter bank before equalization and re-quantization. The signal has a large dynamic range across the full frequency range, owing to variations in the antenna sensitivity, filters in the analog signal chain, and intrinsic spectrum of the sky signal. Radio-frequency interference (RFI) causes strong, narrowband signals, visible as p… view at source ↗
Figure 3
Figure 3. Figure 3: Measured spectra of 8 signals from the OVRO-LWA, after equalization and re-quantization. These are raw outputs from the correlator, prior to any calibration, using one 10 s time integration. The left panel shows the full spectrum, while the right panel zooms in. The spectra exhibit a discontinuous sawtooth pattern that emerges from digital equalization process, as explained in the text. All signals here us… view at source ↗
Figure 4
Figure 4. Figure 4: Left: Re-quantization operation from an E-bit signed number to a b2-bit signed number for b2 = 4. Bit 0 of the re-quantized result corresponds to bit k of the input. Right: Resulting transfer function for input value x and equalization coefficient C. k + b2 − 1 are different, then the value overflows the output representation; in that case, the result is “saturated” at +(2b2−1 − 1) or −(2b2−1 − 1) dependin… view at source ↗
Figure 5
Figure 5. Figure 5: Depiction of the equalization and re-quantization process for a subset of possible values. Each diagonal line corresponds to the same pre-equalization value, from 0 to 29, as labeled. When these values are multiplied by an equalization coefficient (vertical axis) they yield an equalized value (top axis). All equalized values that fall between dashed vertical lines map to the same re-quantized value (bottom… view at source ↗
Figure 6
Figure 6. Figure 6: Histograms showing the number of unique input values that map to each 4-bit output value in re-quantization. The horizontal axes give the equalization coefficient for k = 16. Changes in equalization coefficient cause discrete steps, as values cross the boundaries of the re-quantization bins. Note that, due to saturation, a large number of possible input values map to output values ±7. boundaries of such ra… view at source ↗
Figure 7
Figure 7. Figure 7: Simulated probability distribution before equalization (left) and after equalization (right). The former is for a discrete-valued Gaussian with a standard deviation of σ = 16, as calculated by Equation 3, representing either the real or imaginary part of a simulated filter bank output. At each frequency, it is multiplied by constant equalization coefficient in the equalization step. The equalization functi… view at source ↗
Figure 8
Figure 8. Figure 8: Simulation of the OVRO-LWA signal. Left: The simulation input, corresponding to the filter bank output (see view at source ↗
Figure 9
Figure 9. Figure 9: Simulated signals with linear variation of power with frequency. In the left column, we plot the variance of the simulation input, which is the output of the filter bank in the signal path (see view at source ↗
Figure 10
Figure 10. Figure 10: Example of a piecewise-constant equalization function used for the OVRO-LWA (compare to the previously implemented equalization function, plotted in view at source ↗
Figure 11
Figure 11. Figure 11: Simulated signals with varying numbers of output bits. Here the input signal and equalization function are held constant across all trials and are equivalent to the fourth row in view at source ↗
Figure 12
Figure 12. Figure 12: Simulated signals with varying average signal power. Each signal varies linearly across frequency and has a fractional variation of 100% across 48.97 MHz. The top row has an average signal power of 512 and is equivalent to the fourth row in view at source ↗
Figure 13
Figure 13. Figure 13: Simulated probability distribution of the equalized values before re-quantization, with and without dithering. The left panel does not include dithering and replicates the right panel from view at source ↗
Figure 14
Figure 14. Figure 14: Simulated signals with and without dithering. Once again, the input signal and equalization function are equivalent to the fourth row in view at source ↗
read the original abstract

We identify a systematic distortion of the gain-vs.-frequency function of radio telescopes caused by digital flattening ("whitening") of the signal's spectrum followed by re-quantization, a common pair of processes in the signal processing of modern telescopes. Wide-bandwidth telescopes often have a large variation of signal power over frequency. Flattening of the spectrum allows samples of the channelized signal to be represented in a small number of bits, allowing efficient downstream processing. However, we show that this produces subtle systematic error in the measured spectra. We explore this effect in data from the Owens Valley Radio Observatory's Long Wavelength Array (OVRO-LWA) and through detailed semi-analytic simulations. Although the effect can be small so that it has heretofore been unrecognized, we demonstrate that it produces distortion of the spectrum at a level that is problematic for some science, in particular 21 cm cosmology. Finally, we explore mitigation strategies, showing that the effect can be substantially reduced by careful choice of the gain distribution along the signal path or by incorporating dithering in the re-quantization step.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper claims that digital whitening (spectral flattening) followed by re-quantization, a common processing step in wide-bandwidth radio telescopes, introduces a subtle but systematic distortion in the measured gain-vs-frequency response. This is demonstrated via OVRO-LWA observations and semi-analytic simulations; the distortion is shown to reach levels problematic for 21 cm cosmology, and mitigation via gain distribution choices or dithering is explored.

Significance. If the attribution holds, the result is significant for precision 21 cm cosmology because it identifies a previously unrecognized instrumental systematic capable of producing spectral structure at levels that can contaminate the cosmological signal. The combination of real telescope data with semi-analytic modeling and the explicit discussion of mitigations constitute a practical contribution to instrument design and data analysis in the field.

major comments (2)
  1. [§4] §4 (OVRO-LWA data analysis): the observed spectral distortion is attributed to the whitening-plus-re-quantization sequence, yet the manuscript does not present a control dataset acquired with whitening bypassed under otherwise identical conditions; without this isolation, contributions from analog front-end variations, calibration residuals, or environmental effects cannot be ruled out at the required level.
  2. [§3] §3 (semi-analytic simulations): the model is constructed to embed the whitening and re-quantization steps, so agreement with the OVRO-LWA data demonstrates consistency but does not independently falsify alternative origins; an explicit quantitative error budget comparing predicted versus observed distortion amplitudes (including residual mismatch after mitigation) is needed to establish the mechanism as load-bearing.
minor comments (2)
  1. Figure captions and axis labels should explicitly state the distortion amplitude in units directly comparable to the expected 21 cm signal (e.g., mK or fractional power) to aid readers in assessing impact.
  2. The abstract states the effect 'can be small so that it has heretofore been unrecognized'; a brief literature search or citation to prior 21 cm analyses that may have been affected would strengthen context.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful and constructive review of our manuscript. The comments highlight important aspects of evidence presentation that we address point by point below. We have revised the manuscript accordingly where feasible.

read point-by-point responses

  1. Referee: [§4] §4 (OVRO-LWA data analysis): the observed spectral distortion is attributed to the whitening-plus-re-quantization sequence, yet the manuscript does not present a control dataset acquired with whitening bypassed under otherwise identical conditions; without this isolation, contributions from analog front-end variations, calibration residuals, or environmental effects cannot be ruled out at the required level.

    Authors: We agree that a direct control dataset with whitening disabled would offer the cleanest isolation. However, the OVRO-LWA digital signal processing chain is hard-wired to apply whitening as a standard step for dynamic-range management, and obtaining an otherwise identical control dataset would require non-trivial hardware reconfiguration that was not available during the observations. The semi-analytic simulations isolate the whitening-plus-re-quantization sequence by design and reproduce both the amplitude and spectral shape of the observed distortion. In the revised manuscript we will expand §4 with a dedicated discussion of alternative origins (analog gain ripples, calibration residuals, and environmental effects), showing that none reproduce the specific frequency-dependent structure seen in the data at the observed level. revision: partial

  2. Referee: [§3] §3 (semi-analytic simulations): the model is constructed to embed the whitening and re-quantization steps, so agreement with the OVRO-LWA data demonstrates consistency but does not independently falsify alternative origins; an explicit quantitative error budget comparing predicted versus observed distortion amplitudes (including residual mismatch after mitigation) is needed to establish the mechanism as load-bearing.

    Authors: We accept that a quantitative error budget is required to strengthen the attribution. The revised manuscript will add this analysis to §3, reporting (i) the distortion amplitude predicted by the semi-analytic model, (ii) the amplitude measured in the OVRO-LWA data, (iii) the residual mismatch after each mitigation strategy, and (iv) a direct comparison of how well alternative mechanisms (e.g., analog front-end variations) would match the observed frequency dependence. This will include numerical metrics such as amplitude ratios and goodness-of-fit measures to demonstrate that the whitening model provides the best quantitative description. revision: yes

Circularity Check

0 steps flagged

No circularity; empirical demonstration and simulations are independent of the target claim

full rationale

The paper identifies a spectral distortion mechanism via direct OVRO-LWA observations and semi-analytic modeling of the whitening-plus-re-quantization chain. No step reduces a claimed prediction or first-principles result to its own inputs by definition, fitted parameter, or self-citation chain. The simulations implement the physical model under test rather than presupposing the measured distortion; comparison to real data therefore constitutes external validation, not tautology. The central attribution is presented as an empirical finding open to alternative explanations, with no load-bearing uniqueness theorem or ansatz imported from prior author work. This is the normal case of a self-contained instrumental analysis.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim depends on the domain assumption that the telescope signal chain performs spectrum flattening followed by re-quantization and that the semi-analytic model captures the dominant hardware behavior; no free parameters or new entities are introduced in the abstract.

axioms (1)
  • domain assumption Wide-bandwidth radio telescopes commonly flatten the signal spectrum before re-quantization to enable efficient low-bit sampling.
    Standard practice described in the abstract for modern telescopes.

pith-pipeline@v0.9.0 · 5505 in / 1211 out tokens · 56172 ms · 2026-05-08T15:35:47.610647+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

53 extracted references · 44 canonical work pages · 1 internal anchor

  1. [1]

    E., Alexander, P., et al

    Abdurashidova, Z., Aguirre, J. E., Alexander, P., et al. 2022, HERA Phase I Limits on the Cosmic 21 Cm Signal: Constraints on Astrophysics and Cosmology during the Epoch of Reionization, The Astrophysical Journal, 924, 51, doi:10.3847/1538-4357/ac2ffc

    work page doi:10.3847/1538-4357/ac2ffc 2022

  2. [2]

    Acedo, E. d. L., Trott, C. M., Wayth, R. B., et al. 2017, Spectral Performance of SKA Log-periodic Antennas I: Mitigating Spectral Artefacts in SKA1-LOW 21-Cm Cosmology Experiments, Monthly Notices of the Royal Astronomical Society, 469, 2662, doi:10.1093/mnras/stx904

    work page doi:10.1093/mnras/stx904 2017

  3. [3]

    M., Hallinan, G., Eastwood, M

    Anderson, M. M., Hallinan, G., Eastwood, M. W., et al. 2019, New Limits on the Low-frequency Radio Transient Sky Using 31 Hr of All-sky Data with the OVRO–LWA, The Astrophysical Journal, 886, 123, doi:10.3847/1538-4357/ab4f87

    work page doi:10.3847/1538-4357/ab4f87 2019

  4. [4]

    F., & Pober, J

    Barry, N., Hazelton, B., Sullivan, I., Morales, M. F., & Pober, J. C. 2016, Calibration Requirements for Detecting the 21 Cm Epoch of Reionization Power Spectrum and Implications for the SKA, Monthly Notices of the Royal Astronomical Society, doi:10.1093/mnras/stw1380

    work page doi:10.1093/mnras/stw1380 2016

  5. [5]

    M., et al

    Barry, N., Wilensky, M., Trott, C. M., et al. 2019, Improving the Epoch of Reionization Power Spectrum Results from Murchison Widefield Array Season 1 Observations, The Astrophysical Journal, 884, 1, doi:10.3847/1538-4357/ab40a8

    work page doi:10.3847/1538-4357/ab40a8 2019

  6. [6]

    2023, Delay-Weighted Calibration: Precision Calibration for 21 Cm Cosmology with Resilience to Sky Model Error, Astrophysical Journal, 943, 117, doi:10.3847/1538-4357/acac95

    Byrne, R. 2023, Delay-Weighted Calibration: Precision Calibration for 21 Cm Cosmology with Resilience to Sky Model Error, Astrophysical Journal, 943, 117, doi:10.3847/1538-4357/acac95

    work page doi:10.3847/1538-4357/acac95 2023

  7. [7]

    F., Hazelton, B., et al

    Byrne, R., Morales, M. F., Hazelton, B., et al. 2021a, A Map of Diffuse Radio Emission at 182 MHz to Enhance Epoch of Reionization Observations in the Southern Hemisphere, Monthly Notices of the Royal Astronomical Society, 510, 2011, doi:10.1093/mnras/stab3276

    work page doi:10.1093/mnras/stab3276 2011

  8. [8]

    F., Hazelton, B

    Byrne, R., Morales, M. F., Hazelton, B. J., & Wilensky, M. 2021b, A Unified Calibration Framework for 21 Cm Cosmology, Monthly Notices of the Royal Astronomical Society, 503, 2457, doi:10.1093/mnras/stab647

    work page doi:10.1093/mnras/stab647

  9. [9]

    A., Line, J., Morales, M

    Carroll, P. A., Line, J., Morales, M. F., et al. 2016, A High Reliability Survey of Discrete Epoch of Reionization Foreground Sources in the MWA EoR0 Field, Monthly Notices of the Royal Astronomical Society, doi:10.1093/mnras/stw1599

    work page doi:10.1093/mnras/stw1599 2016

  10. [10]

    E., & Rabiner, L

    Crochiere, R. E., & Rabiner, L. R. 1983, Multirate Digital Signal Processing, 1st edn. (Prentice-Hall)

    1983

  11. [11]

    Cumner, J., Acedo, E. D. L., de Villiers, D. I. L., et al. 2023, Radio Antenna Design for Sky-averaged 21 Cm Cosmology Experiments: The REACH Case, arXiv, doi:10.48550/arXiv.2109.10098 D’Addario, L. R., & Wang, D. 2016, An Integrated Circuit for Radio Astronomy Correlators Supporting Large Arrays of Antennas, Journal of Astronomical Instrumentation, 5, 16...

    work page doi:10.48550/arxiv.2109.10098 2023

  12. [12]

    S., Kohn, S

    Dillon, J. S., Kohn, S. A., Parsons, A. R., et al. 2018, Polarized Redundant-Baseline Calibration for 21 Cm Cosmology Without Adding Spectral Structure, Monthly Notices of the Royal Astronomical Society, 12, 1, doi:10.1093/mnras/sty1060 16 IOP PublishingPASPvv(yyyy) aaaaaa Byrneet al

    work page doi:10.1093/mnras/sty1060 2018

  13. [13]

    S., Lee, M., Ali, Z

    Dillon, J. S., Lee, M., Ali, Z. S., et al. 2020, Redundant-Baseline Calibration of the Hydrogen Epoch of Reionization Array, Monthly Notices of the Royal Astronomical Society, 499, 5840, doi:10.1093/mnras/staa3001

    work page doi:10.1093/mnras/staa3001 2020

  14. [14]

    W., Anderson, M

    Eastwood, M. W., Anderson, M. M., Monroe, R. M., et al. 2018, The Radio Sky at Meter Wavelengths: M-Mode Analysis Imaging with the OVRO-LWA, The Astronomical Journal, 156, 32, doi:10.3847/1538-3881/aac721

    work page doi:10.3847/1538-3881/aac721 2018

  15. [15]

    W., Anderson, M

    Eastwood, M. W., Anderson, M. M., Monroe, R. M., et al. 2019, The 21 Cm Power Spectrum from the Cosmic Dawn: First Results from the OVRO-LWA, The Astronomical Journal, 158, 84, doi:10.3847/1538-3881/ab2629

    work page doi:10.3847/1538-3881/ab2629 2019

  16. [16]

    S., Gehlot, B., et al

    Ewall-Wice, A., Dillon, J. S., Gehlot, B., et al. 2022, Precision Calibration of Radio Interferometers for 21 Cm Cosmology with No Redundancy and Little Knowledge of Antenna Beams and the Radio Sky, The Astrophysical Journal, 938, 151, doi:10.3847/1538-4357/ac87b3

    work page doi:10.3847/1538-4357/ac87b3 2022

  17. [17]

    R., et al

    Fagnoni, N., de Lera Acedo, E., DeBoer, D. R., et al. 2020, Understanding the HERA Phase I Receiver System with Simulations and Its Impact on the Detectability of the EoR Delay Power

    2020

  18. [18]

    Spectrum, Monthly Notices of the Royal Astronomical Society, 500, 1232, doi:10.1093/mnras/staa3268

    work page doi:10.1093/mnras/staa3268

  19. [19]

    R., Oh, S

    Furlanetto, S. R., Peng Oh, S., & Briggs, F. H. 2006, Cosmology at Low Frequencies: The 21 Cm Transition and the High-redshift Universe, Physics Reports, 433, 181, doi:10.1016/j.physrep.2006.08.002

    work page doi:10.1016/j.physrep.2006.08.002 2006

  20. [20]

    L., Bernardi, G., Kenyon, J

    Grobler, T. L., Bernardi, G., Kenyon, J. S., Parsons, A. R., & Smirnov, O. M. 2018, Redundant Interferometric Calibration as a Complex Optimization Problem, Monthly Notices of the Royal Astronomical Society, 476, 2410, doi:10.1093/mnras/sty357

    work page doi:10.1093/mnras/sty357 2018

  21. [21]

    2013, Generating Dithering Noise for Maximum Likelihood Estimation from Quantized Data, Automatica, 49, 554, doi:10.1016/j.automatica.2012.11.028

    Gustafsson, F., & Karlsson, R. 2013, Generating Dithering Noise for Maximum Likelihood Estimation from Quantized Data, Automatica, 49, 554, doi:10.1016/j.automatica.2012.11.028

    work page doi:10.1016/j.automatica.2012.11.028 2013

  22. [22]

    The DSA-2000 -- A Radio Survey Camera

    Hallinan, G., Ravi, V., Weinreb, S., et al. 2019, The DSA-2000 – A Radio Survey Camera, arXiv, doi:10.48550/arXiv.1907.07648

    work page internal anchor Pith review doi:10.48550/arxiv.1907.07648 2019

  23. [23]

    2025, First Results from HERA Phase II, arXiv e-prints

    HERA, Abdurashidova, Z., Adams, T., et al. 2025, First Results from HERA Phase II, arXiv e-prints

    2025

  24. [24]

    J., Barsdell, B

    Kocz, J., Greenhill, L. J., Barsdell, B. R., et al. 2014, A Scalable Hybrid FPGA/GPU FX

    2014

  25. [25]

    Correlator, Journal of Astronomical Instrumentation, 03, 1450002, doi:10.1142/S2251171714500020

    work page doi:10.1142/s2251171714500020

  26. [26]

    1992, Quantization and Dither: A Theoretical

    Lipshitz, S., Wannamaker, R., & Vanderkooy, J. 1992, Quantization and Dither: A Theoretical

    1992

  27. [27]

    Liu, A., & Shaw, J. R. 2020, Data Analysis for Precision 21 Cm Cosmology, Publications of the Astronomical Society of the Pacific, 132, 062001, doi:10.1088/1538-3873/ab5bfd

    work page doi:10.1088/1538-3873/ab5bfd 2020

  28. [28]

    J., Lucas, P

    Liu, A., Tegmark, M., Morrison, S., Lutomirski, A., & Zaldarriaga, M. 2010, Precision Calibration of Radio Interferometers Using Redundant Baselines, Monthly Notices of the Royal Astronomical Society, 408, 1029, doi:10.1111/j.1365-2966.2010.17174.x

    work page doi:10.1111/j.1365-2966.2010.17174.x 2010

  29. [29]

    R., Galvin, T

    Lynch, C. R., Galvin, T. J., Line, J. L. B., et al. 2021, The MWA Long Baseline Epoch of Reionisation Survey—I. Improved Source Catalogue for the EoR 0 Field, Publications of the Astronomical Society of Australia, 38, e057, doi:10.1017/pasa.2021.50

    work page doi:10.1017/pasa.2021.50 2021

  30. [30]

    F., Hazelton, B., Sullivan, I., & Beardsley, A

    Morales, M. F., Hazelton, B., Sullivan, I., & Beardsley, A. 2012, Four Fundamental Foreground Power Spectrum Shapes for 21 Cm Cosmology Observations, The Astrophysical Journal, 752, 137, doi:10.1088/0004-637X/752/2/137

    work page doi:10.1088/0004-637x/752/2/137 2012

  31. [31]

    F., & Wyithe, J

    Morales, M. F., & Wyithe, J. S. B. 2010, Reionization and Cosmology with 21 Cm Fluctuations, Annual Review of Astronomy and Astrophysics, 48, doi:10.1146/annurev-astro-081309-130936 17 IOP PublishingPASPvv(yyyy) aaaaaa Byrneet al

    work page doi:10.1146/annurev-astro-081309-130936 2010

  32. [32]

    S., Crosse, B., Sleap, G., et al

    Morrison, I. S., Crosse, B., Sleap, G., et al. 2023, MWAX: A New Correlator for the Murchison Widefield Array, Publications of the Astronomical Society of Australia, 40, e019, doi:10.1017/pasa.2023.15

    work page doi:10.1017/pasa.2023.15 2023

  33. [33]

    Offringa, A. R. 2016, Compression of Interferometric Radio-Astronomical Data, Astronomy & Astrophysics, 595, A99, doi:10.1051/0004-6361/201629565 O’Hara, O. S. D., Dulwich, F., de Lera Acedo, E., et al. 2024, Understanding Spectral Artefacts in SKA-Low 21-Cm Cosmology Experiments: The Impact of Cable Reflections, Monthly Notices of the Royal Astronomical ...

    work page doi:10.1051/0004-6361/201629565 2016

  34. [34]

    Parsons, A., Backer, D., Siemion, A., et al. 2008, A Scalable Correlator Architecture Based on Modular FPGA Hardware, Reuseable Gateware, and Data Packetization, Publications of the Astronomical Society of the Pacific, 120, 1207, doi:10.1086/593053

    work page doi:10.1086/593053 2008

  35. [35]

    H., Yatawatta, S., Koopmans, L

    Patil, A. H., Yatawatta, S., Koopmans, L. V. E., et al. 2017, Upper Limits on the 21-Cm Epoch of Reionization Power Spectrum from One Night with LOFAR, The Astrophysical Journal, 7, doi:10.3847/1538-4357/aa63e7

    work page doi:10.3847/1538-4357/aa63e7 2017

  36. [36]

    S., Roshi, D

    Prabu, T., Srivani, K. S., Roshi, D. A., et al. 2015, A Digital-Receiver for the Murchison Widefield

    2015

  37. [37]

    Array, Experimental Astronomy, 39, 73, doi:10.1007/s10686-015-9444-3

    work page doi:10.1007/s10686-015-9444-3

  38. [38]

    and Loeb, Abraham

    Pritchard, J. R., & Loeb, A. 2012, 21 Cm Cosmology in the 21st Century, Reports on Progress in Physics, 75, 86901, doi:10.1088/0034-4885/75/8/086901

    work page doi:10.1088/0034-4885/75/8/086901 2012

  39. [39]

    1964, Dither Signals and Their Effect on Quantization Noise, IEEE Transactions on Communication Technology, 12, 162, doi:10.1109/TCOM.1964.1088973

    Schuchman, L. 1964, Dither Signals and Their Effect on Quantization Noise, IEEE Transactions on Communication Technology, 12, 162, doi:10.1109/TCOM.1964.1088973

    work page doi:10.1109/tcom.1964.1088973 1964

  40. [40]

    J., Murphy, E

    Selina, R. J., Murphy, E. J., McKinnon, M., et al. 2018, The Next Generation Very Large Array: A Technical Overview, arXiv, doi:10.48550/arXiv.1806.08405

    work page doi:10.48550/arxiv.1806.08405 2018

  41. [41]

    W., R¨ ottgering, H

    Shimwell, T. W., R¨ ottgering, H. J. A., Best, P. N., et al. 2017, The LOFAR Two-metre Sky Survey - I. Survey Description and Preliminary Data Release, A&A, 598, A104, doi:10.1051/0004-6361/201629313

    work page doi:10.1051/0004-6361/201629313 2017

  42. [42]

    H., Pober, J

    Sims, P. H., Pober, J. C., & Sievers, J. L. 2022, A Bayesian Approach to High Fidelity Interferometric Calibration I: Mathematical Formalism, Monthly Notices of the Royal Astronomical Society, 517, 910, doi:10.1093/mnras/stac1861

    work page doi:10.1093/mnras/stac1861 2022

  43. [43]

    R., Moran, J

    Thompson, A. R., Moran, J. M., & Jr., G. W. S. 2001, Interferometry and Synthesis in Radio Astronomy, 3rd edn. (Springer)

    2001

  44. [44]

    R., DeBoer, D

    Thyagarajan, N., Parsons, A. R., DeBoer, D. R., et al. 2016, Effects of Antenna Beam Chromaticity on Redshifted 21 Cm Power Spectrum and Implications for Hydrogen Epoch of Reionization Array, The Astrophysical Journal, 825, 9, doi:10.3847/0004-637X/825/1/9

    work page doi:10.3847/0004-637x/825/1/9 2016

  45. [45]

    1989, Effect of Various Dither Forms on Quantization Errors of Ideal A/D Converters, IEEE Transactions on Instrumentation and Measurement, 38, 850, doi:10.1109/19.31003

    Wagdy, M. 1989, Effect of Various Dither Forms on Quantization Errors of Ideal A/D Converters, IEEE Transactions on Instrumentation and Measurement, 38, 850, doi:10.1109/19.31003

    work page doi:10.1109/19.31003 1989

  46. [46]

    Wagdy, M., & Goff, M. 1994, Linearizing Average Transfer Characteristics of Ideal ADC’s via Analog and Digital Dither, IEEE Transactions on Instrumentation and Measurement, 43, 146, doi:10.1109/19.293411

    work page doi:10.1109/19.293411 1994

  47. [47]

    Wagdy, M., & Ng, W.-M. 1989, Validity of Uniform Quantization Error Model for Sinusoidal Signals Without and With Dither, IEEE Transactions on Instrumentation and Measurement, 38, 718, doi:10.1109/19.32180

    work page doi:10.1109/19.32180 1989

  48. [48]

    2000, A Theory of Nonsubtractive

    Wannamaker, R., Lipshitz, S., Vanderkooy, J., & Wright, J. 2000, A Theory of Nonsubtractive

    2000

  49. [49]

    Dither, IEEE Transactions on Signal Processing, 48, 499, doi:10.1109/78.823976

    work page doi:10.1109/78.823976

  50. [50]

    2020, Fundamental Physics with the Square Kilometre

    Weltman, A., Bull, P., Camera, S., et al. 2020, Fundamental Physics with the Square Kilometre

    2020

  51. [51]

    Array, Publications of the Astronomical Society of Australia, 37, e002, doi:10.1017/pasa.2019.42

    work page doi:10.1017/pasa.2019.42 2019

  52. [52]

    2010, Quantization Noise (Cambridge University Press), doi:10.1017/CBO9780511754661

    Widrow, B., & Koll´ ar, I. 2010, Quantization Noise (Cambridge University Press), doi:10.1017/CBO9780511754661

    work page doi:10.1017/cbo9780511754661 2010

  53. [53]

    1976, Dither in Nonlinear Systems, IEEE Transactions on Automatic Control, 21, 660, doi:10.1109/TAC.1976.1101357 18

    Zames, G., & Shneydor, N. 1976, Dither in Nonlinear Systems, IEEE Transactions on Automatic Control, 21, 660, doi:10.1109/TAC.1976.1101357 18

    work page doi:10.1109/tac.1976.1101357 1976