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Data for "On-grid compressive sampling for spherical field measurements in acoustics" in The Journal of the Acoustical Society of America.

Published by National Institute of Standards and Technology | National Institute of Standards and Technology | Catalog Last Checked: August 02, 2025 at 03:03 PM | Dataset Last Updated: November 09, 2022
This dataset contains CSV files for the figures in the paper titled "On-grid compressive sampling for spherical field measurements in acoustics" in The Journal of the Acoustical Society of America. In this paper, we derive a compressive sampling method for spherical harmonic/spherical wavefunction or Wigner D-function series with sparse coefficients. Applications of these sparse expansions include spherical field measurements in acoustics and spherical near-field antenna measurements, to name a couple. The figures that this dataset is for are examples demonstrating the following: example acoustic field coefficients in the spherical harmonic/spherical wavefunction basis; relationships between spherical harmonic/spherical wavefunction/Wigner D-function coefficient sparsity and spatial Fourier coefficient sparsity; example compressive sampling reconstruction using our proposed compressive sampling method with and without noise; and comparisons between classical Nyquist sampling and our proposed compressive sampling method.

Resources

35 resources available

  • Figure_3_data_s_D_verus_average_s_F_100_trials.csv

    TEXT/CSV
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  • Figure_10_RelativeError_vs_n_phys_meas_c1a_Fourier_vs_WingerD_grid_dens_1_to_4

    TEXT/CSV
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  • Figure_11_classical_Nyquist_RelativeError_vs_n_meas_with_noise.csv

    TEXT/CSV
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  • Figure_12a_RelativeError_vs_n_phys_meas_vs_grid_dens.csv

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  • Figure_12b_RelativeError_vs_n_phys_meas_vs_grid_dens.csv

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  • Figure_12c_RelativeError_vs_n_phys_meas_vs_grid_dens.csv

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  • Figure_13_coherence_vs_sample_dense_vs_grid_dens.csv

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  • Figure_14a_RelativeError_vs_sample_dense_vs_grid_dens.csv

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  • Figure_14b_RelativeError_vs_sample_dense_vs_grid_dens.csv

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  • Figure_14c_RelativeError_vs_sample_dense_vs_grid_dens.csv

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  • Figure_4a_SW_coefs_DirPat_CUBE_1098Hz.csv

    TEXT/CSV
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  • Figure_4b_SW_coefs_DirPat_CUBE_1400Hz.csv

    TEXT/CSV
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  • Figure_4c_SW_coefs_DirPat_CUBE_1895Hz.csv

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  • Figure_5a_sorted_coefficients_case_1a.csv

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  • Figure_5b_sorted_coefficients_case_1a.csv

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  • Figure_6a_sorted_coefficients_case_1b.csv

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  • Figure_6b_sorted_coefficients_case_1b.csv

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  • Figure_7a_sorted_coefficients_case_1c.csv

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  • Figure_7b_sorted_coefficients_case_1c.csv

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  • Figure_8a_actual_vs_CS_field_C1a.csv

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  • Figure_8b_CS_field_RelativeError_C1a.csv

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  • Figure_9_rel_err_vs_n_phys_meas_Fourier_vs_WingerD.csv

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  • supp_figure_1_sorted_coefficients_case_2a.csv

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  • supp_figure_10_sorted_coefficients_case_3b.csv

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  • supp_figure_11_sorted_coefficients_case_3c.csv

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  • supp_figure_12_sorted_coefficients_case_3c.csv

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  • supp_figure_2_sorted_coefficients_case_2a.csv

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  • supp_figure_3_sorted_coefficients_case_2b.csv

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  • supp_figure_4_sorted_coefficients_case_2b.csv

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  • supp_figure_5_sorted_coefficients_case_2c.csv

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  • supp_figure_6_sorted_coefficients_case_2c.csv

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  • supp_figure_7_sorted_coefficients_case_3a.csv

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  • supp_figure_8_sorted_coefficients_case_3a.csv

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  • supp_figure_9_sorted_coefficients_case_3b.csv

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  • README.txt

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Complete Metadata
@type dcat:Dataset
accessLevel public
accrualPeriodicity irregular
bureauCode 
                                            [
  "006:55"
]
contactPoint 
                                            {
  "fn": "Marc Valdez",
  "hasEmail": "mailto:marc.valdez@nist.gov"
}
description This dataset contains CSV files for the figures in the paper titled "On-grid compressive sampling for spherical field measurements in acoustics" in The Journal of the Acoustical Society of America. In this paper, we derive a compressive sampling method for spherical harmonic/spherical wavefunction or Wigner D-function series with sparse coefficients. Applications of these sparse expansions include spherical field measurements in acoustics and spherical near-field antenna measurements, to name a couple. The figures that this dataset is for are examples demonstrating the following: example acoustic field coefficients in the spherical harmonic/spherical wavefunction basis; relationships between spherical harmonic/spherical wavefunction/Wigner D-function coefficient sparsity and spatial Fourier coefficient sparsity; example compressive sampling reconstruction using our proposed compressive sampling method with and without noise; and comparisons between classical Nyquist sampling and our proposed compressive sampling method.
distribution 
                                            [
  {
    "title": "Figure_3_data_s_D_verus_average_s_F_100_trials.csv",
    "mediaType": "text/csv",
    "description": "This file contains the data for Figure 3, which shows the sorted     concentrations of the Fourier basis sparsity as a function of     Wigner D-function sparsity for different sparsity levels where     the Wigner D-function coefficients are set to 1 at random     positions. The data is organized as described in the header     (first row) of the csv file.",
    "downloadURL": "https://data.nist.gov/od/ds/mds2-2842/Figure_3_data_s_D_verus_average_s_F_100_trials.csv"
  },
  {
    "title": "Figure_10_RelativeError_vs_n_phys_meas_c1a_Fourier_vs_WingerD_grid_dens_1_to_4",
    "mediaType": "text/csv",
    "description": "This file contains the data for figure 10. It shows the     coefficient relative error as a function of measurement number for    Fourier and on-grid Wigner D function based compressive sensing     for the acoustic fields in case 1a as the sampling grid density is    increased. The data is organized as described in the header (first    row) of the csv file.",
    "downloadURL": "https://data.nist.gov/od/ds/mds2-2842/Figure_10_RelativeError_vs_n_phys_meas_c1a_Fourier_vs_WingerD_grid_dens_1_to_4.csv"
  },
  {
    "title": "Figure_11_classical_Nyquist_RelativeError_vs_n_meas_with_noise.csv",
    "mediaType": "text/csv",
    "description": "This file contains the data for figure 11. It shows the relative    error (dB) for classical Fourier sampling as a function of sample    grid density for cases 1a, 2a, and 3a from the paper. The data is    organized as described in the header (first row) of the csv file.",
    "downloadURL": "https://data.nist.gov/od/ds/mds2-2842/Figure_11_classical_Nyquist_RelativeError_vs_n_meas_with_noise.csv"
  },
  {
    "title": "Figure_12a_RelativeError_vs_n_phys_meas_vs_grid_dens.csv",
    "mediaType": "text/csv",
    "description": "This file contains the data for figure 12a. It shows the relative    error (dB) for Fourier based compressive sampling as a function of    sample grid density and number of measurements for case 1a from     the paper. The data is organized as described in the header (first    row) of the csv file.",
    "downloadURL": "https://data.nist.gov/od/ds/mds2-2842/Figure_12a_RelativeError_vs_n_phys_meas_vs_grid_dens.csv"
  },
  {
    "title": "Figure_12b_RelativeError_vs_n_phys_meas_vs_grid_dens.csv",
    "mediaType": "text/csv",
    "description": "This file contains the data for figure 12b. It shows the relative    error (dB) for Fourier based compressive sampling as a function of    sample grid density and number of measurements for case 2a from     the paper. The data is organized as described in the header (first    row) of the csv file.",
    "downloadURL": "https://data.nist.gov/od/ds/mds2-2842/Figure_12b_RelativeError_vs_n_phys_meas_vs_grid_dens.csv"
  },
  {
    "title": "Figure_12c_RelativeError_vs_n_phys_meas_vs_grid_dens.csv",
    "mediaType": "text/csv",
    "description": "This file contains the data for figure 12c. It shows the relative    error (dB) for Fourier based compressive sampling as a function of    sample grid density and number of measurements for cases 3a from     the paper. The data is organized as described in the header (first    row) of the csv file.",
    "downloadURL": "https://data.nist.gov/od/ds/mds2-2842/Figure_12c_RelativeError_vs_n_phys_meas_vs_grid_dens.csv"
  },
  {
    "title": "Figure_13_coherence_vs_sample_dense_vs_grid_dens.csv",
    "mediaType": "text/csv",
    "description": "This file contains the data for figure 13. It shows the average     coherence of the 2DDFT CS measurment matrix as a function of grid    density and average sample number. The average is over 25 trials.     The data is organized as described in the header (first row) of     the csv file.",
    "downloadURL": "https://data.nist.gov/od/ds/mds2-2842/Figure_13_coherence_vs_sample_dense_vs_grid_dens.csv"
  },
  {
    "title": "Figure_14a_RelativeError_vs_sample_dense_vs_grid_dens.csv",
    "mediaType": "text/csv",
    "description": "This file contains the data for figure 14a. It shows the relative    error (dB) for Fourier based compressive sampling as a function of    sample grid density and sample density for cases 1a from the     paper. The data is organized as described in the header (first     row) of the csv file.",
    "downloadURL": "https://data.nist.gov/od/ds/mds2-2842/Figure_14a_RelativeError_vs_sample_dense_vs_grid_dens.csv"
  },
  {
    "title": "Figure_14b_RelativeError_vs_sample_dense_vs_grid_dens.csv",
    "mediaType": "text/csv",
    "description": "This file contains the data for figure 14b. It shows the relative    error (dB) for Fourier based compressive sampling as a function of    sample grid density and sample density for cases 2a from the     paper. The data is organized as described in the header (first     row) of the csv file.",
    "downloadURL": "https://data.nist.gov/od/ds/mds2-2842/Figure_14b_RelativeError_vs_sample_dense_vs_grid_dens.csv"
  },
  {
    "title": "Figure_14c_RelativeError_vs_sample_dense_vs_grid_dens.csv",
    "mediaType": "text/csv",
    "description": "This file contains the data for figure 14c. It shows the relative    error (dB) for Fourier based compressive sampling as a function of    sample grid density and sample density for cases 3a from the     paper. The data is organized as described in the header (first     row) of the csv file.",
    "downloadURL": "https://data.nist.gov/od/ds/mds2-2842/Figure_14c_RelativeError_vs_sample_dense_vs_grid_dens.csv"
  },
  {
    "title": "Figure_4a_SW_coefs_DirPat_CUBE_1098Hz.csv",
    "mediaType": "text/csv",
    "description": "This file contains the data for figure 4a. It shows the magnitude     of the spherical wavefunction coefficients for the DirPat CUBE     driver 1 loudspeaker at 1098Hz. The data is organized as described    in the header (first row) of the csv file.",
    "downloadURL": "https://data.nist.gov/od/ds/mds2-2842/Figure_4a_SW_coefs_DirPat_CUBE_1098Hz.csv"
  },
  {
    "title": "Figure_4b_SW_coefs_DirPat_CUBE_1400Hz.csv",
    "mediaType": "text/csv",
    "description": "This file contains the data for figure 4b. It shows the magnitude     of the spherical wavefunction coefficients for the DirPat CUBE     driver 1 loudspeaker at 1400Hz. The data is organized as described    in the header (first row) of the csv file.",
    "downloadURL": "https://data.nist.gov/od/ds/mds2-2842/Figure_4b_SW_coefs_DirPat_CUBE_1400Hz.csv"
  },
  {
    "title": "Figure_4c_SW_coefs_DirPat_CUBE_1895Hz.csv",
    "mediaType": "text/csv",
    "description": "This file contains the data for figure 4c. It shows the magnitude     of the spherical wavefunction coefficients for the DirPat CUBE     driver 1 loudspeaker at 1895Hz. The data is organized as described    in the header (first row) of the csv file.",
    "downloadURL": "https://data.nist.gov/od/ds/mds2-2842/Figure_4c_SW_coefs_DirPat_CUBE_1895Hz.csv"
  },
  {
    "title": "Figure_5a_sorted_coefficients_case_1a.csv",
    "mediaType": "text/csv",
    "description": "This file contains the data for figure 5a. It shows the relative     magnitude in dB of the sorted Fourier and Wigner D function     coefficients for case 1a as described in the file header and     paper. The data is organized as described in the header (first     row) of the csv file.",
    "downloadURL": "https://data.nist.gov/od/ds/mds2-2842/Figure_5a_sorted_coefficients_case_1a.csv"
  },
  {
    "title": "Figure_5b_sorted_coefficients_case_1a.csv",
    "mediaType": "text/csv",
    "description": "This file contains the data for figure 5b. It shows the     coefficient normalized error in dB of the sorted Fourier and     Wigner D function coefficients for case 1a as described in the    file header and paper. The data is organized as described in the     header (first row) of the csv file.",
    "downloadURL": "https://data.nist.gov/od/ds/mds2-2842/Figure_5b_sorted_coefficients_case_1a.csv"
  },
  {
    "title": "Figure_6a_sorted_coefficients_case_1b.csv",
    "mediaType": "text/csv",
    "description": "This file contains the data for figure 6a. It shows the relative     magnitude in dB of the sorted Fourier and Wigner D function     coefficients for case 1b as described in the file header and     paper. The data is organized as described in the header (first     row) of the csv file.",
    "downloadURL": "https://data.nist.gov/od/ds/mds2-2842/Figure_6a_sorted_coefficients_case_1b.csv"
  },
  {
    "title": "Figure_6b_sorted_coefficients_case_1b.csv",
    "mediaType": "text/csv",
    "description": "This file contains the data for figure 6b. It shows the     coefficient normalized error in dB of the sorted Fourier and     Wigner D function coefficients for case 1b as described in the     file header and paper. The data is organized as described in the     header (first row) of the csv file.",
    "downloadURL": "https://data.nist.gov/od/ds/mds2-2842/Figure_6b_sorted_coefficients_case_1b.csv"
  },
  {
    "title": "Figure_7a_sorted_coefficients_case_1c.csv",
    "mediaType": "text/csv",
    "description": "This file contains the data for figure 7a. It shows the relative    magnitude in dB of the sorted Fourier and Wigner D function     coefficients for case 1c as described in the file header and     paper. The data is organized as described in the header (first     row) of the csv file.",
    "downloadURL": "https://data.nist.gov/od/ds/mds2-2842/Figure_7a_sorted_coefficients_case_1c.csv"
  },
  {
    "title": "Figure_7b_sorted_coefficients_case_1c.csv",
    "mediaType": "text/csv",
    "description": "This file contains the data for figure 7b. It shows the     coefficient normalized error in dB of the sorted Fourier and     Wigner D function coefficients for case 1c as described in the     file header and paper. The data is organized as described in the     header (first row) of the csv file.",
    "downloadURL": "https://data.nist.gov/od/ds/mds2-2842/Figure_7b_sorted_coefficients_case_1c.csv"
  },
  {
    "title": "Figure_8a_actual_vs_CS_field_C1a.csv",
    "mediaType": "text/csv",
    "description": "This file contains the data for figure 8a. It shows the near-field    reconstruction (relative magnitude in dB) using Fourier based     compressive sensing for an acoustic field (case 1a from the     paper). The data is organized as described in the header (first     row) of the csv file.",
    "downloadURL": "https://data.nist.gov/od/ds/mds2-2842/Figure_8a_actual_vs_CS_field_C1a.csv"
  },
  {
    "title": "Figure_8b_CS_field_RelativeError_C1a.csv",
    "mediaType": "text/csv",
    "description": "This file contains the data for figure 8b. It shows the relative      error (dB) of the near-field reconstruction using Fourier based       compressive sensing for an acoustic field (case 1a from the       paper). The data is organized as described in the header (first       row) of the csv file.",
    "downloadURL": "https://data.nist.gov/od/ds/mds2-2842/Figure_8b_CS_field_RelativeError_C1a.csv"
  },
  {
    "title": "Figure_9_rel_err_vs_n_phys_meas_Fourier_vs_WingerD.csv",
    "mediaType": "text/csv",
    "description": "This file contains the data for figure 9. It shows the coefficient    relative error as a function of measurement number for Fourier and    Wigner D function based compressive sensing for acoustic fields     (case 1a, 2a, 3a from the paper). The data is organized as     described in the header (first row) of the csv file.",
    "downloadURL": "https://data.nist.gov/od/ds/mds2-2842/Figure_9_rel_err_vs_n_phys_meas_Fourier_vs_WingerD.csv"
  },
  {
    "title": "supp_figure_1_sorted_coefficients_case_2a.csv",
    "mediaType": "text/csv",
    "description": "This file contains the data for supplemental figure 1. It shows     the relative magnitude in dB of the sorted Fourier and Wigner     D function coefficients for case 2a as described in the file     header and paper. The data is organized as described in the header    (first row) of the csv file.",
    "downloadURL": "https://data.nist.gov/od/ds/mds2-2842/supp_figure_1_sorted_coefficients_case_2a.csv"
  },
  {
    "title": "supp_figure_10_sorted_coefficients_case_3b.csv",
    "mediaType": "text/csv",
    "description": "This file contains the data for supplemental figure 10. It shows     the coefficient normalized error in dB of the sorted Fourier and    Wigner D function coefficients for case 3b as described in the     file header and paper. The data is organized as described in the     header (first row) of the csv file.",
    "downloadURL": "https://data.nist.gov/od/ds/mds2-2842/supp_figure_10_sorted_coefficients_case_3b.csv"
  },
  {
    "title": "supp_figure_11_sorted_coefficients_case_3c.csv",
    "mediaType": "text/csv",
    "description": "This file contains the data for supplemental figure 11. It shows     the relative magnitude in dB of the sorted Fourier and Wigner     D function coefficients for case 3c as described in the file     header and paper. The data is organized as described in the header    (first row) of the csv file.",
    "downloadURL": "https://data.nist.gov/od/ds/mds2-2842/supp_figure_11_sorted_coefficients_case_3c.csv"
  },
  {
    "title": "supp_figure_12_sorted_coefficients_case_3c.csv",
    "mediaType": "text/csv",
    "description": "This file contains the data for supplemental figure 12. It shows     the coefficient normalized error in dB of the sorted Fourier and    Wigner D function coefficients for case 3c as described in the     file header and paper. The data is organized as described in the     header (first row) of the csv file.",
    "downloadURL": "https://data.nist.gov/od/ds/mds2-2842/supp_figure_12_sorted_coefficients_case_3c.csv"
  },
  {
    "title": "supp_figure_2_sorted_coefficients_case_2a.csv",
    "mediaType": "text/csv",
    "description": "This file contains the data for supplemental figure 2. It shows     the coefficient normalized error in dB of the sorted Fourier and     Wigner D function coefficients for case 2a as described in the     file header and paper. The data is organized as described in the     header (first row) of the csv file.",
    "downloadURL": "https://data.nist.gov/od/ds/mds2-2842/supp_figure_2_sorted_coefficients_case_2a.csv"
  },
  {
    "title": "supp_figure_3_sorted_coefficients_case_2b.csv",
    "mediaType": "text/csv",
    "description": "This file contains the data for supplemental figure 3. It shows     the relative magnitude in dB of the sorted Fourier and Wigner     D function coefficients for case 2b as described in the file     header and paper. The data is organized as described in the header    (first row) of the csv file.",
    "downloadURL": "https://data.nist.gov/od/ds/mds2-2842/supp_figure_3_sorted_coefficients_case_2b.csv"
  },
  {
    "title": "supp_figure_4_sorted_coefficients_case_2b.csv",
    "mediaType": "text/csv",
    "description": "This file contains the data for supplemental figure 4. It shows     the coefficient normalized error in dB of the sorted Fourier and     Wigner D function coefficients for case 2b as described in the     file header and paper. The data is organized as described in the     header (first row) of the csv file.",
    "downloadURL": "https://data.nist.gov/od/ds/mds2-2842/supp_figure_4_sorted_coefficients_case_2b.csv"
  },
  {
    "title": "supp_figure_5_sorted_coefficients_case_2c.csv",
    "mediaType": "text/csv",
    "description": "This file contains the data for supplemental figure 5. It shows     the relative magnitude in dB of the sorted Fourier and Wigner     D function coefficients for case 2c as described in the file     header and paper. The data is organized as described in the header    (first row) of the csv file.",
    "downloadURL": "https://data.nist.gov/od/ds/mds2-2842/supp_figure_5_sorted_coefficients_case_2c.csv"
  },
  {
    "title": "supp_figure_6_sorted_coefficients_case_2c.csv",
    "mediaType": "text/csv",
    "description": "This file contains the data for supplemental figure 6. It shows     the coefficient normalized error in dB of the sorted Fourier and     Wigner D function coefficients for case 2c as described in the     file header and paper. The data is organized as described in the     header (first row) of the csv file.",
    "downloadURL": "https://data.nist.gov/od/ds/mds2-2842/supp_figure_6_sorted_coefficients_case_2c.csv"
  },
  {
    "title": "supp_figure_7_sorted_coefficients_case_3a.csv",
    "mediaType": "text/csv",
    "description": "This file contains the data for supplemental figure 7. It shows     the relative magnitude in dB of the sorted Fourier and Wigner     D function coefficients for case 3a as described in the file     header and paper. The data is organized as described in the header    (first row) of the csv file.",
    "downloadURL": "https://data.nist.gov/od/ds/mds2-2842/supp_figure_7_sorted_coefficients_case_3a.csv"
  },
  {
    "title": "supp_figure_8_sorted_coefficients_case_3a.csv",
    "mediaType": "text/csv",
    "description": "This file contains the data for supplemental figure 8. It shows     the coefficient normalized error in dB of the sorted Fourier and     Wigner D function coefficients for case 3a as described in the     file header and paper. The data is organized as described in the    header (first row) of the csv file.",
    "downloadURL": "https://data.nist.gov/od/ds/mds2-2842/supp_figure_8_sorted_coefficients_case_3a.csv"
  },
  {
    "title": "supp_figure_9_sorted_coefficients_case_3b.csv",
    "mediaType": "text/csv",
    "description": "This file contains the data for supplemental figure 9. It shows     the relative magnitude in dB of the sorted Fourier and Wigner     D function coefficients for case 3b as described in the file     header and paper. The data is organized as described in the header    (first row) of the csv file.",
    "downloadURL": "https://data.nist.gov/od/ds/mds2-2842/supp_figure_9_sorted_coefficients_case_3b.csv"
  },
  {
    "title": "README.txt",
    "mediaType": "text/plain",
    "description": "This is a "read me" file that contains and overview of the dataset.",
    "downloadURL": "https://data.nist.gov/od/ds/mds2-2842/README.txt"
  }
]
identifier ark:/88434/mds2-2842
issued 2023-01-11
keyword 
                                            [
  "Wigner D-functions",
  "acoustic fields;",
  "antenna characterization",
  "compressive sampling",
  "compressive sensing",
  "far-field pattern",
  "near-field pattern",
  "sparse signal processing",
  "spherical harmonics"
]
landingPage https://data.nist.gov/od/id/mds2-2842
language 
                                            [
  "en"
]
license https://www.nist.gov/open/license
modified 2022-11-09 00:00:00
programCode 
                                            [
  "006:045"
]
publisher 
                                            {
  "name": "National Institute of Standards and Technology",
  "@type": "org:Organization"
}
references 
                                            [
  "https://doi.org/10.1121/10.0014628"
]
theme 
                                            [
  "Advanced Communications:Wireless (RF)",
  "Mathematics and Statistics:Image and signal processing"
]
title Data for "On-grid compressive sampling for spherical field measurements in acoustics" in The Journal of the Acoustical Society of America.

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