Journal: Scientific Reports

Article Title: i-RheoFT: Fourier transforming sampled functions without artefacts

doi: 10.1038/s41598-021-02922-8

Figure Lengend Snippet: (Top) A single exponential decay function vs. time, representing the relaxation modulus of a single mode Maxwell fluid. (Bottom) A generic function resembling the normalised mean square displacement vs. time of an optically trapped particle suspended into a non-Newtonian fluid. Equations and are represented by a finite number of ‘sampled’ points and a continuous (pink) line. The points are also interpolated by means of three MATLAB built-in interpolation functions: Spline, PCHIP and Makima. The insets show the relative absolute error of each interpolation function with respect of either of Eqs. and , as calculated using Eq. . The time window of the inset encompasses the final three points of the main graph, where the relative error is at its highest.

Article Snippet: Therefore, here we have compared the effectiveness of the following three interpolation functions already built-in MATLAB: a cubic spline data interpolation (Spline) (as the one used in ), a modified Akima piecewise cubic Hermite interpolation (Makima) and Piecewise Cubic Hermite Interpolating Polynomial (PCHIP) .

Techniques:

Journal: Scientific Reports

Article Title: i-RheoFT: Fourier transforming sampled functions without artefacts

doi: 10.1038/s41598-021-02922-8

Figure Lengend Snippet: Mean relative absolute error (MRAE) vs. the density of initial experimental points (DIP) of the three MATLAB built-in interpolation functions: Spline, PCHIP and Makima. (Top) The MRAE is evaluated with respect to Eq. . (Bottom) The MRAE is evaluated with respect to Eq. .

Article Snippet: Therefore, here we have compared the effectiveness of the following three interpolation functions already built-in MATLAB: a cubic spline data interpolation (Spline) (as the one used in ), a modified Akima piecewise cubic Hermite interpolation (Makima) and Piecewise Cubic Hermite Interpolating Polynomial (PCHIP) .

Techniques:

Journal: Scientific Reports

Article Title: i-RheoFT: Fourier transforming sampled functions without artefacts

doi: 10.1038/s41598-021-02922-8

Figure Lengend Snippet: Mean relative absolute error (MRAE) of the frequency-dependent complex moduli determined by Fourier transforming (via Eq. ) the interpolation functions shown in Fig. (top & bottom) for DIP values ranging from 1/4 to 1.

Article Snippet: Therefore, here we have compared the effectiveness of the following three interpolation functions already built-in MATLAB: a cubic spline data interpolation (Spline) (as the one used in ), a modified Akima piecewise cubic Hermite interpolation (Makima) and Piecewise Cubic Hermite Interpolating Polynomial (PCHIP) .

Techniques:

Journal: Scientific Reports

Article Title: i-RheoFT: Fourier transforming sampled functions without artefacts

doi: 10.1038/s41598-021-02922-8

Figure Lengend Snippet: (Top) Eq. and (bottom) Eq. drawn as continuous (pink) lines by using \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$10^4$$\end{document} 10 4 experimental points linearly spaced in time. A white noise having a SNR \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$=50$$\end{document} = 50 is added to the experimental data, which are then interpolated by means of three MATLAB built-in interpolation functions: Spline, PCHIP and Makima. The insets highlight the detrimental effects on the interpolation process due to the presence of noise, both at short and long time scales.

Article Snippet: Therefore, here we have compared the effectiveness of the following three interpolation functions already built-in MATLAB: a cubic spline data interpolation (Spline) (as the one used in ), a modified Akima piecewise cubic Hermite interpolation (Makima) and Piecewise Cubic Hermite Interpolating Polynomial (PCHIP) .

Techniques:

Journal: Scientific Reports

Article Title: i-RheoFT: Fourier transforming sampled functions without artefacts

doi: 10.1038/s41598-021-02922-8

Figure Lengend Snippet: Mean relative absolute error (MRAE) of the frequency-dependent complex moduli determined by Fourier transforming (via Eq. ) the interpolation functions shown in Fig. (top & bottom respectively) for SNR values ranging from 1 to 350 dB. The error bars represent one standard deviation of uncertainty calculated over ten repeats.

Article Snippet: Therefore, here we have compared the effectiveness of the following three interpolation functions already built-in MATLAB: a cubic spline data interpolation (Spline) (as the one used in ), a modified Akima piecewise cubic Hermite interpolation (Makima) and Piecewise Cubic Hermite Interpolating Polynomial (PCHIP) .

Techniques: Standard Deviation