pith. machine review for the scientific record. sign in

arxiv: 2604.06843 · v1 · submitted 2026-04-08 · ⚛️ physics.data-an · cs.NA· math.NA

Recognition: 2 theorem links

· Lean Theorem

Fast and accurate noise removal by curve fitting using orthogonal polynomials

Andrea Gallo Rosso

Authors on Pith no claims yet

Pith reviewed 2026-05-10 18:23 UTC · model grok-4.3

classification ⚛️ physics.data-an cs.NAmath.NA
keywords Savitzky-Golay filtersorthogonal polynomialslocal polynomial smoothingnumerical stabilitycurve fittingnoise removaldata analysisspectral analysis
0
0 comments X

The pith

Reformulating Savitzky-Golay filters with discrete orthogonal polynomials yields fast, stable curve fitting and differentiation.

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

The paper develops algorithms for local polynomial smoothing by switching the underlying basis from monomials to discrete orthogonal Chebyshev polynomials. This reformulation uses the polynomials' recursive definition and matrix symmetries to compute fitting and differentiation matrices with far less memory and better scaling as degree and window size increase. A reader would care because conventional monomial approaches become ill-conditioned and slow for the repeated fits needed in high-volume data tasks such as tuning filters on spectral measurements. If correct, the new methods deliver orders-of-magnitude gains in numerical accuracy while keeping the original smoothing behavior intact. The result is a practical tool for large-scale applications where standard matrix methods break down numerically.

Core claim

By reformulating the problem in terms of discrete orthogonal (Chebyshev) polynomials and exploiting their recursive structure and the intrinsic symmetry properties of the resulting matrices, we derive two algorithms for computing polynomial fitting and differentiation matrices that significantly reduce memory usage and improve scalability with respect to the polynomial degree and window length, achieving orders-of-magnitude improvements in numerical accuracy compared to standard matrix multiplication.

What carries the argument

Discrete orthogonal Chebyshev polynomials, whose recursive definition and symmetry properties are used to construct efficient fitting and differentiation matrices.

If this is right

  • Memory usage drops substantially for higher polynomial degrees and longer data windows.
  • Numerical accuracy improves by orders of magnitude relative to direct matrix multiplication.
  • Execution time gains become possible in large-scale repeated-fitting problems.
  • The methods apply directly to filter optimization in high-resolution spectral analyses such as axion dark matter searches.

Where Pith is reading between the lines

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

  • The same recursive construction could extend to other local polynomial regression tasks that currently rely on monomial bases.
  • Higher polynomial degrees might become usable in practice without the usual numerical breakdown.
  • More precise derivative estimates could result in physics experiments that extract slopes from noisy time series.

Load-bearing premise

Switching from a monomial basis to discrete orthogonal polynomials leaves the exact smoothing and differentiation properties of Savitzky-Golay filters unchanged.

What would settle it

Run both the standard monomial-based Savitzky-Golay procedure and the new orthogonal-polynomial procedure on identical input data and polynomial degree, then verify whether the output smoothed values and derivatives agree to within machine epsilon.

Figures

Figures reproduced from arXiv: 2604.06843 by Andrea Gallo Rosso.

Figure 1
Figure 1. Figure 1: Graphical representation of the computation of the matrix [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Graphical representation of the computation of the matrix [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Magnification of the upper triangle of the right matrix in Figure 2 assuming [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Graphical representation of the computation of the matrix [PITH_FULL_IMAGE:figures/full_fig_p013_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Comparison of the accuracy of Algorithms 0, 1, and 2 in approximating matrix [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Relative difference (56) in the time of computation of [PITH_FULL_IMAGE:figures/full_fig_p015_6.png] view at source ↗
read the original abstract

Local polynomial smoothing is a widespread technique in data analysis, and Savitzky-Golay (SG) filters are one of its most well-known realizations. In real settings, the effectiveness of SG filtering depends critically on proper tuning of its parameters, constrained in turn by repeated polynomial fitting over large data windows and for varying polynomial degrees. Standard implementations based on monomial bases and Vandermonde matrix formulations are known to suffer from ill-conditioning and unfavorable scaling as the problem size increases. In this work, we present a fast and numerically stable method for computing polynomial fitting and differentiation matrices by reformulating the problem in terms of discrete orthogonal (Chebyshev) polynomials. Exploiting their recursive structure and the intrinsic symmetry properties of the resulting matrices, we derive two algorithms designed to reduce computational overhead. Both methods significantly reduce memory usage and improve scalability with respect to the polynomial degree and window length. A discussion of the performance demonstrates that the proposed algorithms achieve orders-of-magnitude improvements in numerical accuracy compared to standard matrix multiplication, while also providing potential gains in execution time for large-scale problems. These features make the approach particularly well suited for applications requiring repeated local polynomial fits, such as the optimization of SG filters in high-resolution spectral analyses, including axion dark matter searches and the ALPHA haloscope.

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

0 major / 3 minor

Summary. The manuscript proposes reformulating Savitzky-Golay polynomial smoothing and differentiation using discrete orthogonal (Chebyshev) polynomials in place of the monomial basis. It derives two algorithms that exploit the recursive structure and symmetry of the resulting matrices to reduce memory usage, improve scalability with polynomial degree and window length, and achieve substantially higher numerical accuracy than direct matrix multiplication with Vandermonde matrices.

Significance. If the numerical claims are borne out by the benchmarks, the work provides a practical, drop-in improvement for repeated local polynomial fits that are central to parameter tuning of SG filters in large-scale spectral analysis. The approach is particularly relevant for high-resolution physics applications such as axion dark matter searches, where ill-conditioned monomial bases limit feasible window sizes and degrees.

minor comments (3)
  1. [Abstract] Abstract: the phrase 'orders-of-magnitude improvements in numerical accuracy' should be accompanied by a brief quantitative statement (e.g., typical condition-number reduction or relative error for a representative degree/window pair) so that readers can immediately gauge the scale of the gain.
  2. [Method] The manuscript should explicitly state (perhaps in §2 or §3) that the orthogonal-polynomial formulation is mathematically equivalent to the classical SG operator in exact arithmetic and that all reported gains arise solely from improved conditioning and recursive evaluation.
  3. [Results] Figure captions and axis labels should include the precise polynomial degree, window length, and floating-point precision used in each timing/accuracy test to allow direct reproduction.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the careful summary of our manuscript, for recognizing its potential significance in high-resolution physics applications such as axion dark matter searches, and for the recommendation of minor revision. We are pleased that the practical advantages of the orthogonal-polynomial reformulation for Savitzky-Golay filters are appreciated.

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper reformulates Savitzky-Golay polynomial fitting and differentiation using discrete orthogonal (Chebyshev) polynomials instead of monomials. Both bases span the identical polynomial space of a given degree, so the least-squares projection, smoothing matrix, and differentiation matrix are mathematically identical in exact arithmetic; any numerical gains arise only from improved Gram-matrix conditioning and recursive evaluation, which are standard, externally established properties of orthogonal polynomials. No equation or algorithm in the derivation defines a target quantity in terms of itself, renames a fitted parameter as a prediction, or relies on a load-bearing self-citation whose validity is internal to the paper. The central claims of improved accuracy and scalability therefore rest on independent mathematical facts rather than on any reduction to the paper's own outputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The approach relies on well-known mathematical properties of discrete orthogonal polynomials; no new free parameters, ad-hoc axioms, or invented entities are introduced.

axioms (1)
  • standard math Discrete orthogonal Chebyshev polynomials satisfy a three-term recurrence and possess symmetry properties that can be exploited for matrix construction.
    Invoked to derive the two algorithms that avoid explicit Vandermonde matrices.

pith-pipeline@v0.9.0 · 5522 in / 1464 out tokens · 69604 ms · 2026-05-10T18:23:05.933146+00:00 · methodology

discussion (0)

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

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

76 extracted references · 43 canonical work pages

  1. [1]

    PeterBruce,AndrewBruce,andPeterGedeck.Practical Statistics for Data Scientists: 50+ Essential Concepts Using R and Python. 2nd. O’Reilly Media, 2020.isbn: 9781492072942

    2020

  2. [2]

    Joel Grus.Data Science from Scratch: First Principles with Python. 2nd. O’Reilly Media, 2021.isbn: 9781492041139

    2021

  3. [3]

    Scharf and Cédric Demeure.Statistical Signal Processing: Detection, Estimation, and Time Series Analysis

    Louis L. Scharf and Cédric Demeure.Statistical Signal Processing: Detection, Estimation, and Time Series Analysis. Addison–Wesley, 1991.isbn: 9780201190380

    1991

  4. [4]

    Lyons.Understanding Digital Signal Processing

    Richard G. Lyons.Understanding Digital Signal Processing. 3rd. Covers fundamentals of digital filtering and spectral methods in signal processing. Prentice Hall, 1997.isbn: 9780137027415

    1997

  5. [5]

    Shumway and David S

    Robert H. Shumway and David S. Stoffer.Time Series Analysis and Its Applications: With R Examples. Springer Texts in Statistics. Springer, 2017.isbn: 9783319524511

    2017

  6. [6]

    Robust Locally Weighted Regression and Smoothing Scatterplots

    William S. Cleveland. “Robust Locally Weighted Regression and Smoothing Scatterplots”. In:Journal of the American Statistical Association74.368 (1979), pp. 829–836.doi:10. 1080/01621459.1979.10481038

    work page arXiv 1979

  7. [7]

    Locally Weighted Regression: An Approach to Regression Analysis by Local Fitting

    William S. Cleveland and Susan J. Devlin. “Locally Weighted Regression: An Approach to Regression Analysis by Local Fitting”. In:Journal of the American Statistical Association 83.403 (1988), pp. 596–610

    1988

  8. [8]

    STL: A Seasonal-Trend Decomposition Procedure Based on Loess (with Discussion)

    Robert B. Cleveland et al. “STL: A Seasonal-Trend Decomposition Procedure Based on Loess (with Discussion)”. In:Journal of Official Statistics6 (1990), pp. 3–73

    1990

  9. [9]

    Properties of Digital Smoothing Polynomial (DISPO) Filters

    Horst Ziegler. “Properties of Digital Smoothing Polynomial (DISPO) Filters”. In:Applied Spectroscopy35.1 (1981), pp. 88–92.doi:10.1366/0003702814731798

    work page doi:10.1366/0003702814731798 1981

  10. [10]

    Smoothing and Differentiation of Data by Simplified Least Squares Procedures

    A. Savitzky and M.J.E. Golay. “Smoothing and Differentiation of Data by Simplified Least Squares Procedures”. In:Analytical Chemistry36.8 (July 1964), pp. 1627–1639.issn: 0003- 2700.doi:10.1021/ac60214a047.url:https://doi.org/10.1021/ac60214a047

    work page doi:10.1021/ac60214a047.url:https://doi.org/10.1021/ac60214a047 1964

  11. [11]

    Savitzky-Golay least-squares polynomial filters in ECG signal processing

    S. Hargittai. “Savitzky-Golay least-squares polynomial filters in ECG signal processing”. In:Computers in Cardiology, 2005. 2005, pp. 763–766.doi:10.1109/CIC.2005.1588216

    work page doi:10.1109/cic.2005.1588216 2005

  12. [12]

    Automatic selection of optimal Savitzky-Golay filter parameters for coro- nary wave intensity analysis

    S. Rivolo et al. “Automatic selection of optimal Savitzky-Golay filter parameters for coro- nary wave intensity analysis”. In:Proceedings of the 36th Annual International Conference of the IEEE Engineering in Medicine and Biology Society. Aug. 2014, pp. 5056–5059

    2014

  13. [13]

    Application of adaptive Savitzky–Golay filter for EEG signal processing

    Deepshikha Acharya et al. “Application of adaptive Savitzky–Golay filter for EEG signal processing”.In:Perspectives in Science8(2016),pp.677–679.issn:2213-0209.doi:https: //doi.org/10.1016/j.pisc.2016.06.056. 16

    work page doi:10.1016/j.pisc.2016.06.056 2016

  14. [14]

    EEG signal enhancement using cascaded S-Golay filter

    S. Agarwal et al. “EEG signal enhancement using cascaded S-Golay filter”. In:Biomedical Signal Processing and Control36 (July 2017), pp. 194–204

    2017

  15. [15]

    Application of Savitzky-Golay digital differentiator for QRS complex detection in an electrocardiographic monitoring system

    E. N. Nishida et al. “Application of Savitzky-Golay digital differentiator for QRS complex detection in an electrocardiographic monitoring system”. In:Proceedings of the IEEE In- ternational Symposium on Medical Measurements and Applications (MeMeA). May 2017, pp. 233–238

    2017

  16. [16]

    Accurate and standardized coronary wave intensity analysis

    S. Rivolo et al. “Accurate and standardized coronary wave intensity analysis”. In:IEEE Transactions on Biomedical Engineering64.5 (May 2017), pp. 1187–1196

    2017

  17. [17]

    Online filtering using piecewise smoothness priors: Application to normal and abnormal electrocardiogram denoising

    R. Sameni. “Online filtering using piecewise smoothness priors: Application to normal and abnormal electrocardiogram denoising”. In:Signal Processing133 (Apr. 2017), pp. 52–63

    2017

  18. [18]

    Quantitative FTIR detection in size-exclusion chromatography

    Keivan Torabi et al. “Quantitative FTIR detection in size-exclusion chromatography”. In:Journal of Chromatography A910.1 (2001), pp. 19–30.issn: 0021-9673.doi:https: //doi.org/10.1016/S0021-9673(00)01122-5.url:https://www.sciencedirect.com/ science/article/pii/S0021967300011225

    work page doi:10.1016/s0021-9673(00)01122-5.url:https://www.sciencedirect.com/ 2001

  19. [19]

    Analysis of ecstasy tablets: comparison of reflectance and transmittance near infrared spectroscopy

    Ralph Carsten Schneider and Karl-Artur Kovar. “Analysis of ecstasy tablets: comparison of reflectance and transmittance near infrared spectroscopy”. In:Forensic Science Inter- national134.2 (2003), pp. 187–195.issn: 0379-0738.doi:https://doi.org/10.1016/ S0379-0738(03)00125-7

    2003

  20. [20]

    Optimizing Savitzky–Golay parameters for im- proving spectral resolution and quantification in infrared spectroscopy

    Boris Zimmermann and Achim Kohler. “Optimizing Savitzky–Golay parameters for im- proving spectral resolution and quantification in infrared spectroscopy”. In:Applied Spec- troscopy67.8 (2013), pp. 892–902.issn: 0003-7028.doi:10.1366/12-06723

    work page doi:10.1366/12-06723 2013

  21. [21]

    A modified empirical mode decomposition algorithm in TDLAS for gas detection

    Y. Meng et al. “A modified empirical mode decomposition algorithm in TDLAS for gas detection”. In:IEEE Photonics Journal6.1 (Dec. 2014)

    2014

  22. [22]

    Savitzky-Golay Parameter Optimization by using Linear Discriminant Analysis for FTIR Spectra

    Dyah Kurniawati Agustika et al. “Savitzky-Golay Parameter Optimization by using Linear Discriminant Analysis for FTIR Spectra”. In:2022 IEEE 7th Forum on Research and Technologies for Society and Industry Innovation (RTSI). 2022, pp. 123–128.doi:10 . 1109/RTSI55261.2022.9905171

    work page arXiv 2022

  23. [23]

    TIMESAT—a program for analyzing time-series of satel- lite sensor data

    Per Jönsson and Lars Eklundh. “TIMESAT—a program for analyzing time-series of satel- lite sensor data”. In:Computers & Geosciences30.8 (2004), pp. 833–845.issn: 0098- 3004.doi:https://doi.org/10.1016/j.cageo.2004.05.006.url:https://www. sciencedirect.com/science/article/pii/S0098300404000974

    work page doi:10.1016/j.cageo.2004.05.006.url:https://www 2004

  24. [24]

    Spectrogram enhancement using multiple window Savitzky-Golay (MWSG) filter for robust bird sound detection

    N. R. Koluguri, G. N. Meenakshi, and P. K. Ghosh. “Spectrogram enhancement using multiple window Savitzky-Golay (MWSG) filter for robust bird sound detection”. In: IEEE/ACM Transactions on Audio, Speech, and Language Processing25.6 (June 2017), pp. 1183–1192

    2017

  25. [25]

    Spatial-temporaldynamicmonitoringofvegetationrecoveryafterthe WenchuanEarthquake

    W.YangandW.Qi.“Spatial-temporaldynamicmonitoringofvegetationrecoveryafterthe WenchuanEarthquake”.In:IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing10.3 (Mar. 2017), pp. 868–876

    2017

  26. [26]

    Meteorological Drought Trend Analysis and Forecasting Using a Hybrid SG-CEEMDAN-ARIMA-LSTM Model Based on SPI from Rain Gauge Data

    S. Sibiya et al. “Meteorological Drought Trend Analysis and Forecasting Using a Hybrid SG-CEEMDAN-ARIMA-LSTM Model Based on SPI from Rain Gauge Data”. In:Natural Hazards and Earth System Sciences26.1 (2026), pp. 315–342.doi:10.5194/nhess-26- 315-2026.url:https://nhess.copernicus.org/articles/26/315/2026/. 17

    work page doi:10.5194/nhess-26- 2026

  27. [27]

    Experiments and analysis of fis- sion product release in HEU-fuelled SLOWPOKE-2 reactors

    A.C. Harnden-Gillis, L.G.I. Bennett, and B.J. Lewis. “Experiments and analysis of fis- sion product release in HEU-fuelled SLOWPOKE-2 reactors”. In:Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment345.3 (1994), pp. 520–527.issn: 0168-9002.doi:https : / / doi . org/10.1016/0168-90...

    work page doi:10.1016/0168-9002(94)90510-x 1994

  28. [28]

    Recursivedigitalfilterswithtunablelagandleadcharacteristicsforproportional- differential control

    H.Kennedy.“Recursivedigitalfilterswithtunablelagandleadcharacteristicsforproportional- differential control”. In:IEEE Transactions on Control Systems Technology23.6 (Nov. 2015), pp. 2369–2374

    2015

  29. [29]

    Savitzky-Golay filter for reactivity calculation

    D. Suescún-Díaz, H. F. Bonilla-Londoño, and J. H. Figueroa-Jiménez. “Savitzky-Golay filter for reactivity calculation”. In:Journal of Nuclear Science and Technology53.7 (July 2016), pp. 944–950

    2016

  30. [30]

    Application of Higham and Savitzky-Golay Filters to Nuclear Spectra

    Vansha Kher et al. “Application of Higham and Savitzky-Golay Filters to Nuclear Spectra”. In:Soft Computing Applications. Ed. by Valentina Emilia Balas, Lakhmi C. Jain, and Marius Mircea Balas. Cham: Springer International Publishing, 2018, pp. 487–496.isbn: 978-3-319-62521-8

    2018

  31. [31]

    OnSavitzky-Golayfilteringforonlineconditionmonitoring of transformer on-load tap changer

    J.Seo,H.Ma,andT.K.Saha.“OnSavitzky-Golayfilteringforonlineconditionmonitoring of transformer on-load tap changer”. In:IEEE Transactions on Power Delivery33.4 (Aug. 2018), pp. 1689–1698

    2018

  32. [32]

    A Savitzky-Golay filtering perspective of dynamic feature computation

    S. R. Krishnan, M. Magimai-Doss, and C. S. Seelamantula. “A Savitzky-Golay filtering perspective of dynamic feature computation”. In:IEEE Signal Processing Letters20.3 (Mar. 2013), pp. 281–284

    2013

  33. [33]

    CP Conservation in the Presence of Instantons

    R. D. Peccei and Helen R. Quinn. “CP Conservation in the Presence of Instantons”. In: Phys. Rev. Lett.38 (1977), pp. 1440–1443.doi:10.1103/PhysRevLett.38.1440

    work page doi:10.1103/physrevlett.38.1440 1977

  34. [34]

    H., Jedamzik, K., & Pogosian, L

    R. D. Peccei and Helen R. Quinn. “Constraints Imposed by CP Conservation in the Pres- ence of Instantons”. In:Phys. Rev. D16 (1977), pp. 1791–1797.doi:10.1103/PhysRevD. 16.1791

    work page doi:10.1103/physrevd 1977

  35. [35]

    Weinberg, Phys

    Steven Weinberg. “A New Light Boson?” In:Phys. Rev. Lett.40 (1978), pp. 223–226.doi: 10.1103/PhysRevLett.40.223

    work page doi:10.1103/physrevlett.40.223 1978

  36. [36]

    Wilczek, Phys

    Frank Wilczek. “Problem of Strong P and T Invariance in the Presence of Instantons”. In: Phys. Rev. Lett.40 (1978), pp. 279–282.doi:10.1103/PhysRevLett.40.279

    work page doi:10.1103/physrevlett.40.279 1978

  37. [37]

    Weak Interaction Singlet and Strong CP Invariance

    Jihn E. Kim. “Weak Interaction Singlet and Strong CP Invariance”. In:Phys. Rev. Lett. 43 (1979), p. 103.doi:10.1103/PhysRevLett.43.103

    work page doi:10.1103/physrevlett.43.103 1979

  38. [38]

    Can Confinement Ensure Natural CP Invariance of Strong Interactions?

    M. A. Shifman, A. I. Vainshtein, and V. I. Zakharov. “Can Confinement Ensure Natural CP Invariance of Strong Interactions?” In:Phys. Lett. B78 (1978), pp. 443–446.doi: 10.1016/0370-2693(80)90209-6

    work page doi:10.1016/0370-2693(80)90209-6 1978

  39. [39]

    A Simple Solution to the Strong CP Problem with a Harmless Axion

    Michael Dine, Willy Fischler, and Mark Srednicki. “A Simple Solution to the Strong CP Problem with a Harmless Axion”. In:Phys. Lett. B104 (1981), pp. 199–202.doi:10 . 1016/0370-2693(81)90590-6

    1981

  40. [40]

    On Possible Suppression of the Axion Hadron Interactions. (In Rus- sian)

    A. R. Zhitnitsky. “On Possible Suppression of the Axion Hadron Interactions. (In Rus- sian)”. In:Sov. J. Nucl. Phys.31 (1980), p. 260

    1980

  41. [41]

    Schneider, B

    Igor G. Irastorza and Javier Redondo. “New experimental approaches in the search for axion-like particles”. In:Prog. Part. Nucl. Phys.102 (2018), pp. 89–159.doi:10.1016/j. ppnp.2018.05.003. arXiv:1801.08127 [hep-ph]. 18

    work page doi:10.1016/j 2018

  42. [42]

    Direct detection of dark matter – APPEC committee report

    J. Billard et al. “Direct detection of dark matter – APPEC committee report”. In:J. Phys. G49.4 (2022), p. 040501.doi:10.1088/1361-6471/ac5754. arXiv:2104.07634 [hep-ex]

    work page doi:10.1088/1361-6471/ac5754 2022

  43. [43]

    Laboratory searches for galactic axions

    Igor G. Irastorza. “Laboratory searches for galactic axions”. In:Rept. Prog. Phys.84.10 (2021), p. 106901.doi:10.1088/1361-6633/ac0d1c. arXiv:2103.12400 [hep-ph]

    work page doi:10.1088/1361-6633/ac0d1c 2021

  44. [44]

    Axion dark matter: How to see it?

    Yannis K. Semertzidis and Seongtae Youn. “Axion dark matter: How to see it?” In:SciPost Phys. Proc.2 (2019), p. 021.doi:10.21468/SciPostPhysProc.2.021. arXiv:1904.04168 [hep-ph]

    work page doi:10.21468/scipostphysproc.2.021 2019

  45. [45]

    Douglas Adams et al., eds.Axion Dark Matter. Vol. 1. CERN Yellow Reports: School Proceedings. Geneva: CERN, 2021.doi:10.17181/CERN.97QY-CKH9

    work page doi:10.17181/cern.97qy-ckh9 2021

  46. [46]

    David J. E. Marsh, Igor G. Irastorza, and Javier Redondo, eds.The Physics of Axions. Cham: Springer, 2022.doi:10.1007/978-3-030-95852-7

    work page doi:10.1007/978-3-030-95852-7 2022

  47. [47]

    Searching for dark matter with plasma haloscopes

    Alexander J. Millar et al. “Searching for dark matter with plasma haloscopes”. In:Phys. Rev. D107.5 (2023), p. 055013.doi:10.1103/PhysRevD.107.055013. arXiv:2210.00017 [hep-ph]

    work page doi:10.1103/physrevd.107.055013 2023

  48. [48]

    Charmousis, E.J

    Pierre Sikivie. “Experimental Tests of the Invisible Axion”. In:Phys. Rev. Lett.51 (1983). [Erratum: Phys.Rev.Lett. 52, 695 (1984)], pp. 1415–1417.doi:10.1103/PhysRevLett. 51.1415

    work page doi:10.1103/physrevlett 1983

  49. [49]

    Detection Rates for ’Invisible’ Axion Searches

    Pierre Sikivie. “Detection Rates for ’Invisible’ Axion Searches”. In:Phys. Rev. D32 (1985). [Erratum: Phys.Rev.D 36, 974 (1987)], pp. 2988–2991.doi:10.1103/PhysRevD.32.2988

    work page doi:10.1103/physrevd.32.2988 1985

  50. [50]

    Revealing the Dark Matter Halo with Axion Direct Detection,

    Joshua W. Foster, Nicholas L. Rodd, and Benjamin R. Safdi. “Revealing the Dark Matter Halo with Axion Direct Detection”. In:Phys. Rev. D97.12 (2018), p. 123006.doi:10. 1103/PhysRevD.97.123006. arXiv:1711.10489 [astro-ph.CO]

    work page arXiv 2018

  51. [51]

    Improved analysis framework for axion dark matter searches

    D. A. Palken et al. “Improved analysis framework for axion dark matter searches”. In: Phys. Rev. D101.12 (2020), p. 123011.doi:10 . 1103 / PhysRevD . 101 . 123011. arXiv: 2003.08510 [astro-ph.IM]

    work page arXiv 2020

  52. [52]

    Sequential hypothesis testing for axion haloscopes

    Andrea Gallo Rosso, Sara Algeri, and Jan Conrad. “Sequential hypothesis testing for axion haloscopes”. In:Phys. Rev. D108.2 (2023), p. 023003.doi:10 . 1103 / PhysRevD . 108 . 023003. arXiv:2210.16095 [physics.data-an]

    work page arXiv 2023

  53. [53]

    Directionalaxiondetection

    SimonSchmidetal.“Directionalaxiondetection”.In:Phys. Rev. D105.8(2022),p.083022. doi:10.1103/PhysRevD.105.083022. arXiv:2202.08209 [hep-ph]

    work page doi:10.1103/physrevd.105.083022 2022

  54. [54]

    Directional detection of axion dark matter

    Zhuo Yi, Malte Buschmann, and Benjamin R. Safdi. “Directional detection of axion dark matter”. In:Phys. Rev. D108.4 (2023), p. 043024.doi:10.1103/PhysRevD.108.043024. arXiv:2301.10789 [hep-ph]

    work page doi:10.1103/physrevd.108.043024 2023

  55. [55]

    Window Selection of the Savitzky–Golay Filters for Signal Recovery From Noisy Measurements

    Mohammad Sadeghi, Fereidoon Behnia, and Rouhollah Amiri. “Window Selection of the Savitzky–Golay Filters for Signal Recovery From Noisy Measurements”. In:IEEE Trans- actions on Instrumentation and Measurement69.8 (2020), pp. 5418–5427.doi:10.1109/ TIM.2020.2966310

    work page arXiv 2020

  56. [56]

    On the Selection of Optimum Savitzky-Golay Filters

    Sunder Ram Krishnan and Chandra Sekhar Seelamantula. “On the Selection of Optimum Savitzky-Golay Filters”. In:IEEE Transactions on Signal Processing61.2 (2013), pp. 380– 391.doi:10.1109/TSP.2012.2225055. 19

    work page doi:10.1109/tsp.2012.2225055 2013

  57. [57]

    Selecting the optimal conditions of Savitzky–Golay filter for fNIRS signal

    Md. Asadur Rahman, Mohd Abdur Rashid, and Mohiuddin Ahmad. “Selecting the optimal conditions of Savitzky–Golay filter for fNIRS signal”. In:Biocybernetics and Biomedical Engineering39.3 (2019), pp. 624–637.issn: 0208-5216.doi:https://doi.org/10.1016/ j.bbe.2019.06.004.url:https://www.sciencedirect.com/science/article/pii/ S0208521618305667

    2019

  58. [58]

    AutomaticSelectionofOptimalSavitzky– Golay Smoothing

    GabrielVivó-TruyolsandPeterJ.Schoenmakers.“AutomaticSelectionofOptimalSavitzky– Golay Smoothing”. In:Analytical Chemistry78.13 (2006), pp. 4598–4608.issn: 0003-2700. doi:10.1021/ac0600196.url:https://doi.org/10.1021/ac0600196

    work page doi:10.1021/ac0600196.url:https://doi.org/10.1021/ac0600196 2006

  59. [59]

    URLhttps://doi.org/10.1214/aos/1176345338

    Charles M. Stein. “Estimation of the Mean of a Multivariate Normal Distribution”. In: The Annals of Statistics9.6 (1981), pp. 1135–1151.doi:10.1214/aos/1176345632.url: https://doi.org/10.1214/aos/1176345632

    work page doi:10.1214/aos/1176345632.url: 1981

  60. [60]

    Parameter selection for smoothing splines using Stein’s Unbiased Risk Estimator

    Sepideh Seifzadeh et al. “Parameter selection for smoothing splines using Stein’s Unbiased Risk Estimator”. In:The 2011 International Joint Conference on Neural Networks. 2011, pp. 2733–2740.doi:10.1109/IJCNN.2011.6033577

    work page doi:10.1109/ijcnn.2011.6033577 2011

  61. [61]

    Cambridge University Press, 1961

    Philip George Guest.Numerical Methods of Curve Fitting. Cambridge University Press, 1961

    1961

  62. [62]

    What Is a Savitzky-Golay Filter? [Lecture Notes]

    Ronald W. Schafer. “What Is a Savitzky-Golay Filter? [Lecture Notes]”. In:IEEE Signal Processing Magazine28.4 (2011), pp. 111–117.doi:10 . 1109 / MSP . 2011 . 941097.url: http://andrewd.ces.clemson.edu/courses/cpsc881/papers/Sch11_whatIsSG.pdf

    2011

  63. [63]

    Cambridge, USA: Cambridge University Press, 1992.isbn: 978-0521431088.url:https: //numerical.recipes/book.html

    WilliamH.Pressetal.Numerical Recipes: The Art of Scientific Computing.Secondedition. Cambridge, USA: Cambridge University Press, 1992.isbn: 978-0521431088.url:https: //numerical.recipes/book.html

    1992

  64. [64]

    Press et al.Numerical Recipes: The Art of Scientific Computing

    William H. Press et al.Numerical Recipes: The Art of Scientific Computing. Third edition. Cambridge, USA: Cambridge University Press, 2011.isbn: 978-0521880688.url:https: //numerical.recipes/book.html

    2011

  65. [65]

    Shohat.Théorie générale des polynômes orthogonaux de Tchebichef

    J. Shohat.Théorie générale des polynômes orthogonaux de Tchebichef. Vol. 66. Mémorial des sciences mathématiques. Gauthier-Villars, 1934.url:http://www.numdam.org/item/ MSM_1934__66__1_0.pdf

    1934

  66. [66]

    Providence, Rhode Island, USA: American Math- ematical Society, 1939.url:https://people.math.osu.edu/nevai.1/AT/SZEGO/szego= szego1975=ops=OCR.pdf

    Gabor Szegö.Orthogonal Polynomials. Providence, Rhode Island, USA: American Math- ematical Society, 1939.url:https://people.math.osu.edu/nevai.1/AT/SZEGO/szego= szego1975=ops=OCR.pdf

    1939

  67. [67]

    Some Orthogonal Methods of Curve and Surface Fitting

    J. H. Cadwell and D. Williams. “Some Orthogonal Methods of Curve and Surface Fitting”. In:Comput. J.4 (1961), pp. 260–264.doi:10.1093/comjnl/4.3.260

    work page doi:10.1093/comjnl/4.3.260 1961

  68. [68]

    POLYNOMIAL CURVE FITTING WITH CONSTRAINT

    J. Peck. “POLYNOMIAL CURVE FITTING WITH CONSTRAINT”. In:Siam Review4 (1962), pp. 135–141.doi:10.1137/1004031

    work page doi:10.1137/1004031 1962

  69. [69]

    A method of storing the orthogonal polynomials used for curve and surface fitting

    D. G. Hayes. “A method of storing the orthogonal polynomials used for curve and surface fitting”. In:Comput. J.12 (1969), pp. 148–150.doi:10.1093/comjnl/12.2.148

    work page doi:10.1093/comjnl/12.2.148 1969

  70. [70]

    Fan and I

    J. Fan and I. Gijbels.Local Polynomial Modelling and Its Applications. 1st. Monographs on Statistics and Applied Probability. New York: Chapman & Hall/CRC, 1996.isbn: 9780203748725

    1996

  71. [71]

    Controlled accuracy for discrete Chebyshev polynomials

    Albertus C. den Brinker. “Controlled accuracy for discrete Chebyshev polynomials”. In: 2020 28th European Signal Processing Conference (EUSIPCO). 2021, pp. 2279–2283.doi: 10.23919/Eusipco47968.2020.9287544. 20

    work page doi:10.23919/eusipco47968.2020.9287544 2020

  72. [72]

    Chebyshev.Théorie des mécanismes connus sous le nom de parallélogrammes

    Pafnutij L. Chebyshev.Théorie des mécanismes connus sous le nom de parallélogrammes. French. ETH-Bibliothek Zürich, Rar 23506. Public Domain Mark. St. Petersbourg: Im- primerie de l’Académie Impériale des Sciences, 1853.url:https://doi.org/10.3931/e- rara-120037

    work page doi:10.3931/e-

  73. [73]

    Sur l’interpolation

    P.L. Tchebychef. “Sur l’interpolation”. In:Zapiski Akademii Nauk4 (1864)

  74. [74]

    2026.url:https://github.com/gallorosso/polfit

    Andrea Gallo Rosso.polfit. 2026.url:https://github.com/gallorosso/polfit

    2026

  75. [75]

    Nikiforov, Vasilii B

    Arnold F. Nikiforov, Vasilii B. Uvarov, and Sergei K. Suslov.Classical Orthogonal Poly- nomials of a Discrete Variable. Heidelberg: Springer Berlin, 2012.isbn: 978-3642747502. url:https://link.springer.com/book/10.1007/978-3-642-74748-9

    work page doi:10.1007/978-3-642-74748-9 2012

  76. [76]

    Version v6-18-02

    Rene Brun et al.root-project/root: v6.18/02. Version v6-18-02. Aug. 2019.doi:10.5281/ zenodo.3895860.url:https://doi.org/10.5281/zenodo.3895860. 21 Algorithm 2:Computation ofA n Data:N,n < N 1buffer←[ ⃗0,⃗0,⃗0,⃗0,⃗0] 2a 0 ←a 1 ←[0, . . . ,0]▷ ⃗Ai,ℓ−2, ⃗Ai,ℓ−1 in(52) 3i max ← ⌊N/2⌋+ (Nmod 2)−1 4fori←0toi max do /* Initializea 0,a 1 */ 5ifi= 0(first row)the...

    work page doi:10.5281/zenodo.3895860 2019