About this Dataset

Data For "On-grid Compressive Sampling For Spherical Field Measurements In Acoustics" In The Journal Of The Acoustical Society Of America.

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.
Organization: National Institute of Standards and Technology
Last updated: 2023-02-23T03:44:27.766871
Tags: acoustic-fields, antenna-characterization, compressive-sampling, compressive-sensing, far-field-pattern, near-field-pattern, sparse-signal-processing, spherical-harmonics, wigner-d-functions

Tables

Figure 10 RelativeError Vs N Phys Meas C1a Fourier Vs WingerD Grid Dens 1 To 4

@usgov.national_institute_of_standard_data_for_on_grid_compre_31ae5c2c.figure_10_relativeerror_vs_n_phys_meas_c1a_fourier_vs__b0ab1361

18.75 kB
41 rows
12 columns

CREATE TABLE figure_10_relativeerror_vs_n_phys_meas_c1a_fourier_vs__b0ab1361 (
  "mean_number_of_unique_physical_measurments_no_relevant_109cae50" DOUBLE  -- Mean Number Of Unique "physical Measurments" (no Relevant Units) - See Section 4 E Paragraph 1 - Averaged Over 25 Trials With A Grid Density Of 1 Times The Nyquist Rate.,
  "mean_number_of_unique_physical_measurments_no_relevant_4a3d649d" DOUBLE  -- Mean Number Of Unique "physical Measurments" (no Relevant Units) - See Section 4 E Paragraph 1 - Averaged Over 25 Trials With A Grid Density Of 2 Times The Nyquist Rate.,
  "mean_number_of_unique_physical_measurments_no_relevant_44553f3a" DOUBLE  -- Mean Number Of Unique "physical Measurments" (no Relevant Units) - See Section 4 E Paragraph 1 - Averaged Over 25 Trials With A Grid Density Of 4 Times The Nyquist Rate.,
  "mean_number_of_unique_physical_measurments_no_relevant_c7f365ce" DOUBLE  -- Mean Number Of Unique "physical Measurments" (no Relevant Units) - See Section 4 E Paragraph 1 - Averaged Over 25 Trials With A Grid Density Of 8 Times The Nyquist Rate.,
  "relative_error_db_of_sw_coefficients_defined_in_equati_ca962873" DOUBLE  -- Relative Error (dB) Of SW Coefficients Defined In Equation 36 Recovered Using Of Fourier CS For Case 1a Defined In Section 4 C As A Function Of Mean Number Of "physical Measurments" With A Grid Density Of 1 Times The Nyquist Rate.,
  "relative_error_db_of_sw_coefficients_defined_in_equati_ace622bb" DOUBLE  -- Relative Error (dB) Of SW Coefficients Defined In Equation 36 Recovered Using Of Fourier CS For Case 1a Defined In Section 4 C As A Function Of Mean Number Of "physical Measurments" With A Grid Density Of 2 Times The Nyquist Rate.,
  "relative_error_db_of_sw_coefficients_defined_in_equati_b4a65363" DOUBLE  -- Relative Error (dB) Of SW Coefficients Defined In Equation 36 Recovered Using Of Fourier CS For Case 1a Defined In Section 4 C As A Function Of Mean Number Of "physical Measurments" With A Grid Density Of 4 Times The Nyquist Rate.,
  "relative_error_db_of_sw_coefficients_defined_in_equati_0d0c89dd" DOUBLE  -- Relative Error (dB) Of SW Coefficients Defined In Equation 36 Recovered Using Of Fourier CS For Case 1a Defined In Section 4 C As A Function Of Mean Number Of "physical Measurments" With A Grid Density Of 8 Times The Nyquist Rate.,
  "relative_error_db_of_sw_coefficients_defined_in_equati_dfd1d2e0" DOUBLE  -- Relative Error (dB) Of SW Coefficients Defined In Equation 36 Recovered Using Of On-grid Wigner D-function CS (see Paragraph 2 Of Section 4 E) For Case 1a Defined In Section 4 C As A Function Of Mean Number Of "physical Measurments" With A Grid Density Of 1 Times The Nyquist Rate.,
  "relative_error_db_of_sw_coefficients_defined_in_equati_a7142724" DOUBLE  -- Relative Error (dB) Of SW Coefficients Defined In Equation 36 Recovered Using Of On-grid Wigner D-function CS (see Paragraph 2 Of Section 4 E) For Case 1a Defined In Section 4 C As A Function Of Mean Number Of "physical Measurments" With A Grid Density Of 2 Times The Nyquist Rate.,
  "relative_error_db_of_sw_coefficients_defined_in_equati_fd5da6c7" DOUBLE  -- Relative Error (dB) Of SW Coefficients Defined In Equation 36 Recovered Using Of On-grid Wigner D-function CS (see Paragraph 2 Of Section 4 E) For Case 1a Defined In Section 4 C As A Function Of Mean Number Of "physical Measurments" With A Grid Density Of 4 Times The Nyquist Rate.,
  "relative_error_db_of_sw_coefficients_defined_in_equati_f14ffcf5" DOUBLE  -- Relative Error (dB) Of SW Coefficients Defined In Equation 36 Recovered Using Of On-grid Wigner D-function CS (see Paragraph 2 Of Section 4 E) For Case 1a Defined In Section 4 C As A Function Of Mean Number Of "physical Measurments" With A Grid Density Of 8 Times The Nyquist Rate.
);

Figure 11 Classical Nyquist RelativeError Vs N Meas With Noise

@usgov.national_institute_of_standard_data_for_on_grid_compre_31ae5c2c.figure_11_classical_nyquist_relativeerror_vs_n_meas_with_noise

6.41 kB
25 rows
4 columns

CREATE TABLE figure_11_classical_nyquist_relativeerror_vs_n_meas_with_noise (
  "sample_density_fraction_of_nyquis_rate_no_relevant_uni_e05ab2fc" DOUBLE  -- Sample Density (Fraction Of Nyquis Rate (no Relevant Units)) For Reconstruction Using Classical Nyquist Sampling Approach (see Section 4 F Paragraph 1).,
  "mean_relative_error_db_of_sw_coefficients_defined_in_e_970c9099" DOUBLE  -- Mean Relative Error (dB) Of SW Coefficients Defined In Equation 36 Recovered Using Classical Nyquist Sampling With Measurment Noise (see Section 4 F Paragraph 1) For Case 1a Defined In Section 4 C As A Function Of Sample Density (also See Section 4 F Paragraph 1). Relative Error Is Ageraged Over 25 Trials.,
  "mean_relative_error_db_of_sw_coefficients_defined_in_e_b241a84a" DOUBLE  -- Mean Relative Error (dB) Of SW Coefficients Defined In Equation 36 Recovered Using Classical Nyquist Sampling With Measurment Noise (see Section 4 F Paragraph 1) For Case 2a Defined In Section 4 C As A Function Of Sample Density (also See Section 4 F Paragraph 1). Relative Error Is Ageraged Over 25 Trials.,
  "mean_relative_error_db_of_sw_coefficients_defined_in_e_3e2922c7" DOUBLE  -- Mean Relative Error (dB) Of SW Coefficients Defined In Equation 36 Recovered Using Classical Nyquist Sampling With Measurment Noise (see Section 4 F Paragraph 1) For Case 3a Defined In Section 4 C As A Function Of Sample Density (also See Section 4 F Paragraph 1). Relative Error Is Ageraged Over 25 Trials.
);

Figure 12a RelativeError Vs N Phys Meas Vs Grid Dens

@usgov.national_institute_of_standard_data_for_on_grid_compre_31ae5c2c.figure_12a_relativeerror_vs_n_phys_meas_vs_grid_dens

9.89 kB
400 rows
3 columns

CREATE TABLE figure_12a_relativeerror_vs_n_phys_meas_vs_grid_dens (
  "grid_sample_density_fraction_of_nyquis_rate_no_relevan_d871220c" DOUBLE  -- Grid Sample Density (Fraction Of Nyquis Rate (no Relevant Units)) - See Section 4 F Paragraph 2 - From Which Random Samples Are Taken From.,
  "mean_number_of_unique_physical_measurments_in_fourier__6ae13767" DOUBLE  -- Mean Number Of Unique "physical Measurments" In Fourier CS (see Section 4.5 Paragraph 1) Averaged Over 25 Trials.,
  "relative_error_db_of_sw_coefficients_defined_in_equati_bcb5c958" DOUBLE  -- Relative Error (dB) Of SW Coefficients Defined In Equation 36 Recovered Using Of Fourier CS For Case 1a Defined In Section 4 C As A Function Of Sample Density And Mean Number Of "physical Measurments."
);

Figure 12b RelativeError Vs N Phys Meas Vs Grid Dens

@usgov.national_institute_of_standard_data_for_on_grid_compre_31ae5c2c.figure_12b_relativeerror_vs_n_phys_meas_vs_grid_dens

9.84 kB
400 rows
3 columns

CREATE TABLE figure_12b_relativeerror_vs_n_phys_meas_vs_grid_dens (
  "grid_sample_density_fraction_of_nyquis_rate_no_relevan_d871220c" DOUBLE  -- Grid Sample Density (Fraction Of Nyquis Rate (no Relevant Units)) - See Section 4 F Paragraph 2 - From Which Random Samples Are Taken From.,
  "mean_number_of_unique_physical_measurments_in_fourier__6ae13767" DOUBLE  -- Mean Number Of Unique "physical Measurments" In Fourier CS (see Section 4.5 Paragraph 1) Averaged Over 25 Trials.,
  "relative_error_db_of_sw_coefficients_defined_in_equati_2e75f9be" DOUBLE  -- Relative Error (dB) Of SW Coefficients Defined In Equation 36 Recovered Using Of Fourier CS For Case 2a Defined In Section 4 C As A Function Of Sample Density And Mean Number Of "physical Measurments."
);

Figure 12c RelativeError Vs N Phys Meas Vs Grid Dens

@usgov.national_institute_of_standard_data_for_on_grid_compre_31ae5c2c.figure_12c_relativeerror_vs_n_phys_meas_vs_grid_dens

9.81 kB
400 rows
3 columns

CREATE TABLE figure_12c_relativeerror_vs_n_phys_meas_vs_grid_dens (
  "grid_sample_density_fraction_of_nyquis_rate_no_relevan_d871220c" DOUBLE  -- Grid Sample Density (Fraction Of Nyquis Rate (no Relevant Units)) - See Section 4 F Paragraph 2 - From Which Random Samples Are Taken From.,
  "mean_number_of_unique_physical_measurments_in_fourier__6ae13767" DOUBLE  -- Mean Number Of Unique "physical Measurments" In Fourier CS (see Section 4.5 Paragraph 1) Averaged Over 25 Trials.,
  "relative_error_db_of_sw_coefficients_defined_in_equati_a13bbb48" DOUBLE  -- Relative Error (dB) Of SW Coefficients Defined In Equation 36 Recovered Using Of Fourier CS For Case 3a Defined In Section 4 C As A Function Of Sample Density And Mean Number Of "physical Measurments."
);

Figure 13 Coherence Vs Sample Dense Vs Grid Dens

@usgov.national_institute_of_standard_data_for_on_grid_compre_31ae5c2c.figure_13_coherence_vs_sample_dense_vs_grid_dens

10.61 kB
400 rows
3 columns

CREATE TABLE figure_13_coherence_vs_sample_dense_vs_grid_dens (
  "grid_sample_density_fraction_of_nyquis_rate_no_relevan_d871220c" DOUBLE  -- Grid Sample Density (Fraction Of Nyquis Rate (no Relevant Units)) - See Section 4 F Paragraph 2 - From Which Random Samples Are Taken From.,
  "mean_number_of_unique_physical_measurments_in_fourier__b5eb92f6" DOUBLE  -- Mean Number Of Unique "physical Measurments" In Fourier CS (see Section 4 E Paragraph 1) Averaged Over 25 Trials.,
  "average_coherence_see_equation_37_of_2d_fourier_measur_5037a581" DOUBLE  -- Average Coherence (see Equation 37) Of 2D Fourier Measurment Matrix As A Function Of Sample Density And Mean Number Of "physical Measurments." Averaged Over 25 Trials For Each Sample Density And Measurment Number Selection.
);

Figure 14a RelativeError Vs Sample Dense Vs Grid Dens

@usgov.national_institute_of_standard_data_for_on_grid_compre_31ae5c2c.figure_14a_relativeerror_vs_sample_dense_vs_grid_dens

11.03 kB
400 rows
3 columns

CREATE TABLE figure_14a_relativeerror_vs_sample_dense_vs_grid_dens (
  "grid_sample_density_fraction_of_nyquis_rate_no_relevan_d871220c" DOUBLE  -- Grid Sample Density (Fraction Of Nyquis Rate (no Relevant Units)) - See Section 4 F Paragraph 2 - From Which Random Samples Are Taken From.,
  "measurment_sample_density_no_relevent_units_defined_in_c77c65c1" DOUBLE  -- Measurment Sample Density (no Relevent Units) Defined In Section 4 F Paragraph 4 Averaged Over 25 Trials.,
  "relative_error_db_of_sw_coefficients_defined_in_equati_bcb5c958" DOUBLE  -- Relative Error (dB) Of SW Coefficients Defined In Equation 36 Recovered Using Of Fourier CS For Case 1a Defined In Section 4 C As A Function Of Sample Density And Mean Number Of "physical Measurments."
);

Figure 14b RelativeError Vs Sample Dense Vs Grid Dens

@usgov.national_institute_of_standard_data_for_on_grid_compre_31ae5c2c.figure_14b_relativeerror_vs_sample_dense_vs_grid_dens

11.1 kB
400 rows
3 columns

CREATE TABLE figure_14b_relativeerror_vs_sample_dense_vs_grid_dens (
  "grid_sample_density_fraction_of_nyquis_rate_no_relevan_d871220c" DOUBLE  -- Grid Sample Density (Fraction Of Nyquis Rate (no Relevant Units)) - See Section 4 F Paragraph 2 - From Which Random Samples Are Taken From.,
  "measurment_sample_density_no_relevent_units_defined_in_c77c65c1" DOUBLE  -- Measurment Sample Density (no Relevent Units) Defined In Section 4 F Paragraph 4 Averaged Over 25 Trials.,
  "relative_error_db_of_sw_coefficients_defined_in_equati_2e75f9be" DOUBLE  -- Relative Error (dB) Of SW Coefficients Defined In Equation 36 Recovered Using Of Fourier CS For Case 2a Defined In Section 4 C As A Function Of Sample Density And Mean Number Of "physical Measurments."
);

Figure 14c RelativeError Vs Sample Dense Vs Grid Dens

@usgov.national_institute_of_standard_data_for_on_grid_compre_31ae5c2c.figure_14c_relativeerror_vs_sample_dense_vs_grid_dens

11.09 kB
400 rows
3 columns

CREATE TABLE figure_14c_relativeerror_vs_sample_dense_vs_grid_dens (
  "grid_sample_density_fraction_of_nyquis_rate_no_relevan_d871220c" DOUBLE  -- Grid Sample Density (Fraction Of Nyquis Rate (no Relevant Units)) - See Section 4 F Paragraph 2 - From Which Random Samples Are Taken From.,
  "measurment_sample_density_no_relevent_units_defined_in_c77c65c1" DOUBLE  -- Measurment Sample Density (no Relevent Units) Defined In Section 4 F Paragraph 4 Averaged Over 25 Trials.,
  "relative_error_db_of_sw_coefficients_defined_in_equati_a13bbb48" DOUBLE  -- Relative Error (dB) Of SW Coefficients Defined In Equation 36 Recovered Using Of Fourier CS For Case 3a Defined In Section 4 C As A Function Of Sample Density And Mean Number Of "physical Measurments."
);

Figure 3 Data S D Verus Average S F 100 Trials

@usgov.national_institute_of_standard_data_for_on_grid_compre_31ae5c2c.figure_3_data_s_d_verus_average_s_f_100_trials

5.35 kB
52 rows
4 columns

CREATE TABLE figure_3_data_s_d_verus_average_s_f_100_trials (
  "wigner_d_function_sparsity" BIGINT,
  "sparsity_in_the_wigner_d_function_basis_s_d_no_relevant_units" DOUBLE  -- Sparsity In The Wigner D-function Basis S D (no Relevant Units),
  "average_fourier_basis_sparsity" VARCHAR,
  "n__s_f_no_relevant_units_average_is_over_100_trials_as_087dcd91" VARCHAR  -- S F (no Relevant Units). Average Is Over 100 Trials As Specified In The Text Of Section 4 B.
);

Figure 4a SW Coefs DirPat CUBE 1098Hz

@usgov.national_institute_of_standard_data_for_on_grid_compre_31ae5c2c.figure_4a_sw_coefs_dirpat_cube_1098hz

6.77 kB
496 rows
3 columns

CREATE TABLE figure_4a_sw_coefs_dirpat_cube_1098hz (
  "spherical_wavefunction_coefficeint_index_m_no_relevant_c5869c89" BIGINT  -- Spherical Wavefunction Coefficeint Index M (no Relevant Units). See Paragraph Following Equation 11.,
  "spherical_wavefunction_coefficeint_index_n_no_relevant_65f98c1b" BIGINT  -- Spherical Wavefunction Coefficeint Index N (no Relevant Units). See Paragraph Following Equation 11.,
  "spherical_wavefunction_coefficient_relative_magnitude__138ba939" DOUBLE  -- Spherical Wavefunction Coefficient Relative Magnitude (dB) - Defined In Eq. 48 - For The IEM Loudspeaker Cube Driver 1 At 1098 Hz. See The Third Paragraph Of Section 4 C.
);

Figure 4b SW Coefs DirPat CUBE 1400Hz

@usgov.national_institute_of_standard_data_for_on_grid_compre_31ae5c2c.figure_4b_sw_coefs_dirpat_cube_1400hz

6.78 kB
496 rows
3 columns

CREATE TABLE figure_4b_sw_coefs_dirpat_cube_1400hz (
  "spherical_wavefunction_coefficeint_index_m_no_relevant_c5869c89" BIGINT  -- Spherical Wavefunction Coefficeint Index M (no Relevant Units). See Paragraph Following Equation 11.,
  "spherical_wavefunction_coefficeint_index_n_no_relevant_65f98c1b" BIGINT  -- Spherical Wavefunction Coefficeint Index N (no Relevant Units). See Paragraph Following Equation 11.,
  "spherical_wavefunction_coefficient_relative_magnitude__b0cac6d7" DOUBLE  -- Spherical Wavefunction Coefficient Relative Magnitude (dB) - Defined In Eq. 48 - For The IEM Loudspeaker Cube Driver 1 At 1400 Hz. See The Third Paragraph Of Section 4 C.
);

Figure 4c SW Coefs DirPat CUBE 1895Hz

@usgov.national_institute_of_standard_data_for_on_grid_compre_31ae5c2c.figure_4c_sw_coefs_dirpat_cube_1895hz

6.82 kB
496 rows
3 columns

CREATE TABLE figure_4c_sw_coefs_dirpat_cube_1895hz (
  "spherical_wavefunction_coefficeint_index_m_no_relevant_c5869c89" BIGINT  -- Spherical Wavefunction Coefficeint Index M (no Relevant Units). See Paragraph Following Equation 11.,
  "spherical_wavefunction_coefficeint_index_n_no_relevant_65f98c1b" BIGINT  -- Spherical Wavefunction Coefficeint Index N (no Relevant Units). See Paragraph Following Equation 11.,
  "spherical_wavefunction_coefficient_relative_magnitude__cb56049f" DOUBLE  -- Spherical Wavefunction Coefficient Relative Magnitude (dB) - Defined In Eq. 48 - For The IEM Loudspeaker Cube Driver 1 At 1895 Hz. See The Third Paragraph Of Section 4 C.
);

Figure 5a Sorted Coefficients Case 1a

@usgov.national_institute_of_standard_data_for_on_grid_compre_31ae5c2c.figure_5a_sorted_coefficients_case_1a

17.2 kB
917 rows
4 columns

CREATE TABLE figure_5a_sorted_coefficients_case_1a (
  "sorted_position_wigner_d_function_coefficient_no_relev_ffc6f2ab" VARCHAR  -- Sorted Position Wigner D Function Coefficient (no Relevant Units).,
  "sorted_wigner_d_coefficient_relative_magnitude_db_defi_d24c7c56" VARCHAR  -- Sorted Wigner D Coefficient Relative Magnitude (dB) - Defined In Equation 32 - For Case 1a Defined In Section 4 C.,
  "sorted_position_wigner_d_function_coefficient_no_relev_fea36b70" BIGINT  -- Sorted Position Wigner D Function Coefficient (no Relevant Units)..1,
  "sorted_fourier_coefficient_relative_magnitude_db_defin_46b60c22" DOUBLE  -- Sorted Fourier Coefficient Relative Magnitude (dB) - Defined In Equation 32 - For Case 1a Defined In Section 4 C.
);

Figure 5b Sorted Coefficients Case 1a

@usgov.national_institute_of_standard_data_for_on_grid_compre_31ae5c2c.figure_5b_sorted_coefficients_case_1a

32.68 kB
917 rows
6 columns

CREATE TABLE figure_5b_sorted_coefficients_case_1a (
  "number_of_wigner_d_coefficients_kept_no_relevant_units" VARCHAR  -- Number Of Wigner D Coefficients Kept (no Relevant Units).,
  "normalized_error_of_kept_wigner_d_coefficeints_db_defi_91425a60" VARCHAR  -- Normalized Error Of Kept Wigner D Coefficeints (dB) - Defined In Equation 33 - For Case 1a Defined In Section 4 C.,
  "number_of_fourier_coefficients_kept_no_relevant_units" BIGINT  -- Number Of Fourier Coefficients Kept (no Relevant Units).,
  "normalized_error_of_kept_fourier_coefficeints_db_defin_daa09e21" DOUBLE  -- Normalized Error Of Kept Fourier Coefficeints (dB) - Defined In Equation 33 - For Case 1a Defined In Section 4 C.,
  "number_of_fourier_coefficients_kept_no_relevant_units_1" BIGINT  -- Number Of Fourier Coefficients Kept (no Relevant Units)..1,
  "normalized_error_of_kept_fourier_coefficeints_transfor_00219782" DOUBLE  -- Normalized Error Of Kept Fourier Coefficeints Transformed Back To Wigner D Basis (dB) - Defined In Equation 33 - For Case 1a Defined In Section 4 C.
);

Figure 6a Sorted Coefficients Case 1b

@usgov.national_institute_of_standard_data_for_on_grid_compre_31ae5c2c.figure_6a_sorted_coefficients_case_1b

41.31 kB
2,809 rows
4 columns

CREATE TABLE figure_6a_sorted_coefficients_case_1b (
  "sorted_position_wigner_d_function_coefficient_no_relev_ffc6f2ab" VARCHAR  -- Sorted Position Wigner D Function Coefficient (no Relevant Units).,
  "sorted_wigner_d_coefficient_relative_magnitude_db_defi_251ff756" VARCHAR  -- Sorted Wigner D Coefficient Relative Magnitude (dB) - Defined In Equation 32 - For Case 1b Defined In Section 4 C.,
  "sorted_position_wigner_d_function_coefficient_no_relev_fea36b70" BIGINT  -- Sorted Position Wigner D Function Coefficient (no Relevant Units)..1,
  "sorted_fourier_coefficient_relative_magnitude_db_defin_2734f867" DOUBLE  -- Sorted Fourier Coefficient Relative Magnitude (dB) - Defined In Equation 32 - For Case 1b Defined In Section 4 C.
);

Figure 6b Sorted Coefficients Case 1b

@usgov.national_institute_of_standard_data_for_on_grid_compre_31ae5c2c.figure_6b_sorted_coefficients_case_1b

83.94 kB
2,809 rows
6 columns

CREATE TABLE figure_6b_sorted_coefficients_case_1b (
  "number_of_wigner_d_coefficients_kept_no_relevant_units" VARCHAR  -- Number Of Wigner D Coefficients Kept (no Relevant Units).,
  "normalized_error_of_kept_wigner_d_coefficeints_db_defi_513be46a" VARCHAR  -- Normalized Error Of Kept Wigner D Coefficeints (dB) - Defined In Equation 33 - For Case 1b Defined In Section 4 C.,
  "number_of_fourier_coefficients_kept_no_relevant_units" BIGINT  -- Number Of Fourier Coefficients Kept (no Relevant Units).,
  "normalized_error_of_kept_fourier_coefficeints_db_defin_28848ed6" DOUBLE  -- Normalized Error Of Kept Fourier Coefficeints (dB) - Defined In Equation 33 - For Case 1b Defined In Section 4 C.,
  "number_of_fourier_coefficients_kept_no_relevant_units_1" BIGINT  -- Number Of Fourier Coefficients Kept (no Relevant Units)..1,
  "normalized_error_of_kept_fourier_coefficeints_transfor_e26df07a" DOUBLE  -- Normalized Error Of Kept Fourier Coefficeints Transformed Back To Wigner D Basis (dB) - Defined In Equation 33 - For Case 1b Defined In Section 4 C.
);

Figure 7a Sorted Coefficients Case 1c

@usgov.national_institute_of_standard_data_for_on_grid_compre_31ae5c2c.figure_7a_sorted_coefficients_case_1c

65.68 kB
4,699 rows
4 columns

CREATE TABLE figure_7a_sorted_coefficients_case_1c (
  "sorted_position_wigner_d_function_coefficient_no_relev_ffc6f2ab" VARCHAR  -- Sorted Position Wigner D Function Coefficient (no Relevant Units).,
  "sorted_wigner_d_coefficient_relative_magnitude_db_defi_3e04703e" VARCHAR  -- Sorted Wigner D Coefficient Relative Magnitude (dB) - Defined In Equation 32 - For Case 1c Defined In Section 4 C.,
  "sorted_position_wigner_d_function_coefficient_no_relev_fea36b70" BIGINT  -- Sorted Position Wigner D Function Coefficient (no Relevant Units)..1,
  "sorted_fourier_coefficient_relative_magnitude_db_defin_2b4723c8" DOUBLE  -- Sorted Fourier Coefficient Relative Magnitude (dB) - Defined In Equation 32 - For Case 1c Defined In Section 4 C.
);

Figure 7b Sorted Coefficients Case 1c

@usgov.national_institute_of_standard_data_for_on_grid_compre_31ae5c2c.figure_7b_sorted_coefficients_case_1c

136.05 kB
4,699 rows
6 columns

CREATE TABLE figure_7b_sorted_coefficients_case_1c (
  "number_of_wigner_d_coefficients_kept_no_relevant_units" VARCHAR  -- Number Of Wigner D Coefficients Kept (no Relevant Units).,
  "normalized_error_of_kept_wigner_d_coefficeints_db_defi_617417fe" VARCHAR  -- Normalized Error Of Kept Wigner D Coefficeints (dB) - Defined In Equation 33 - For Case 1c Defined In Section 4 C.,
  "number_of_fourier_coefficients_kept_no_relevant_units" BIGINT  -- Number Of Fourier Coefficients Kept (no Relevant Units).,
  "normalized_error_of_kept_fourier_coefficeints_db_defin_beade21f" DOUBLE  -- Normalized Error Of Kept Fourier Coefficeints (dB) - Defined In Equation 33 - For Case 1c Defined In Section 4 C.,
  "number_of_fourier_coefficients_kept_no_relevant_units_1" BIGINT  -- Number Of Fourier Coefficients Kept (no Relevant Units)..1,
  "normalized_error_of_kept_fourier_coefficeints_transfor_6e238a96" DOUBLE  -- Normalized Error Of Kept Fourier Coefficeints Transformed Back To Wigner D Basis (dB) - Defined In Equation 33 - For Case 1c Defined In Section 4 C.
);

Figure 8a Actual Vs CS Field C1a

@usgov.national_institute_of_standard_data_for_on_grid_compre_31ae5c2c.figure_8a_actual_vs_cs_field_c1a

16.93 kB
501 rows
3 columns

CREATE TABLE figure_8a_actual_vs_cs_field_c1a (
  "polar_measurment_angle_theta_radians_azimuthal_angle_i_e6f5dc9a" DOUBLE  -- Polar Measurment Angle Theta (radians) - Azimuthal Angle Is Phi = 0 Radians.,
  "relative_magnitude_of_field_db_defined_in_equation_34__f2077817" DOUBLE  -- Relative Magnitude Of Field (dB) - Defined In Equation 34 - True Near Field Generate By Spherical Wavefunction Coefficients From The IEM Loudspeaker Cube Driver 1 Operating At 1098Hz. The Near Field Is At A Radius Of R=0.75m.,
  "relative_magnitude_of_field_db_defined_in_equation_34__b5b3e6db" DOUBLE  -- Relative Magnitude Of Field (dB) - Defined In Equation 34 - For The Near Field Generate By Spherical Wavefunction Coefficients Recovered According To Lemma 6 And Theorem 7 Simulated Measurments Of The IEM Cube Driver 1 Operating At 1098Hz Taken A Radius Of R=0.75m.
);

Figure 8b CS Field RelativeError C1a

@usgov.national_institute_of_standard_data_for_on_grid_compre_31ae5c2c.figure_8b_cs_field_relativeerror_c1a

11.32 kB
501 rows
2 columns

CREATE TABLE figure_8b_cs_field_relativeerror_c1a (
  "polar_measurment_angle_theta_radians_azimuthal_angle_i_e6f5dc9a" DOUBLE  -- Polar Measurment Angle Theta (radians) - Azimuthal Angle Is Phi = 0 Radians.,
  "relative_error_db_defined_in_equation_35_for_the_near__4f04cd63" DOUBLE  -- Relative Error (dB) - Defined In Equation 35 - For The Near Field Generate By Spherical Wavefunction Coefficients Recovered According To Lemma 6 And Theorem 7 Using Simulated Measurments Of The IEM Cube Driver 1 Operating At 1098Hz Taken A Radius Of R=0.75m.
);

Figure 9 Rel Err Vs N Phys Meas Fourier Vs WingerD

@usgov.national_institute_of_standard_data_for_on_grid_compre_31ae5c2c.figure_9_rel_err_vs_n_phys_meas_fourier_vs_wingerd

11.45 kB
41 rows
7 columns

CREATE TABLE figure_9_rel_err_vs_n_phys_meas_fourier_vs_wingerd (
  "mean_number_of_unique_physical_measurments_no_relevant_4764d22b" DOUBLE  -- Mean Number Of Unique "physical Measurments" (no Relevant Units) - See Section 4 E Paragraph 1 - Averaged Over 25 Trials.,
  "relative_error_db_of_sw_coefficients_defined_in_equati_7185f190" DOUBLE  -- Relative Error (dB) Of SW Coefficients Defined In Equation 36 Recovered Using Of Fourier CS For Case 1a Defined In Section 4 C As A Function Of Mean Number Of "physical Measurments.",
  "relative_error_db_of_sw_coefficients_defined_in_equati_f3cf3498" DOUBLE  -- Relative Error (dB) Of SW Coefficients Defined In Equation 36 Recovered Using Of On-grid Wigner D-function CS (see Paragraph 2 Of Section 4 E) For Case 1a Defined In Section 4 C As A Function Of Mean Number Of "physical Measurments.",
  "relative_error_db_of_sw_coefficients_defined_in_equati_40109657" DOUBLE  -- Relative Error (dB) Of SW Coefficients Defined In Equation 36 Recovered Using Of Fourier CS For Case 2a Defined In Section 4 C As A Function Of Mean Number Of "physical Measurments.",
  "relative_error_db_of_sw_coefficients_defined_in_equati_8415d18c" DOUBLE  -- Relative Error (dB) Of SW Coefficients Defined In Equation 36 Recovered Using Of On-grid Wigner D-function CS (see Paragraph 2 Of Section 4 E) For Case 2a Defined In Section 4 C As A Function Of Mean Number Of "physical Measurments.",
  "relative_error_db_of_sw_coefficients_defined_in_equati_ab84be30" DOUBLE  -- Relative Error (dB) Of SW Coefficients Defined In Equation 36 Recovered Using Of Fourier CS For Case 3a Defined In Section 4 C As A Function Of Mean Number Of "physical Measurments.",
  "relative_error_db_of_sw_coefficients_defined_in_equati_285f615d" DOUBLE  -- Relative Error (dB) Of SW Coefficients Defined In Equation 36 Recovered Using Of On-grid Wigner D-function CS (see Paragraph 2 Of Section 4 E) For Case 3a Defined In Section 4 C As A Function Of Mean Number Of "physical Measurments."
);

Supp Figure 10 Sorted Coefficients Case 3b

@usgov.national_institute_of_standard_data_for_on_grid_compre_31ae5c2c.supp_figure_10_sorted_coefficients_case_3b

84.31 kB
2,809 rows
6 columns

CREATE TABLE supp_figure_10_sorted_coefficients_case_3b (
  "number_of_wigner_d_coefficients_kept_no_relevant_units" VARCHAR  -- Number Of Wigner D Coefficients Kept (no Relevant Units).,
  "normalized_error_of_kept_wigner_d_coefficeints_db_defi_5220b2c0" VARCHAR  -- Normalized Error Of Kept Wigner D Coefficeints (dB) - Defined In Equation 33 - For Case 3b Defined In Section 4 C.,
  "number_of_fourier_coefficients_kept_no_relevant_units" BIGINT  -- Number Of Fourier Coefficients Kept (no Relevant Units).,
  "normalized_error_of_kept_fourier_coefficeints_db_defin_db9671e0" DOUBLE  -- Normalized Error Of Kept Fourier Coefficeints (dB) - Defined In Equation 33 - For Case 3b Defined In Section 4 C.,
  "number_of_fourier_coefficients_kept_no_relevant_units_1" BIGINT  -- Number Of Fourier Coefficients Kept (no Relevant Units)..1,
  "normalized_error_of_kept_fourier_coefficeints_transfor_9f577d65" DOUBLE  -- Normalized Error Of Kept Fourier Coefficeints Transformed Back To Wigner D Basis (dB) - Defined In Equation 33 - For Case 3b Defined In Section 4 C.
);

Supp Figure 11 Sorted Coefficients Case 3c

@usgov.national_institute_of_standard_data_for_on_grid_compre_31ae5c2c.supp_figure_11_sorted_coefficients_case_3c

65.77 kB
4,699 rows
4 columns

CREATE TABLE supp_figure_11_sorted_coefficients_case_3c (
  "sorted_position_wigner_d_function_coefficient_no_relev_ffc6f2ab" VARCHAR  -- Sorted Position Wigner D Function Coefficient (no Relevant Units).,
  "sorted_wigner_d_coefficient_relative_magnitude_db_defi_d5a978bb" VARCHAR  -- Sorted Wigner D Coefficient Relative Magnitude (dB) - Defined In Equation 32 - For Case 3c Defined In Section 4 C.,
  "sorted_position_wigner_d_function_coefficient_no_relev_fea36b70" BIGINT  -- Sorted Position Wigner D Function Coefficient (no Relevant Units)..1,
  "sorted_fourier_coefficient_relative_magnitude_db_defin_86e5a677" DOUBLE  -- Sorted Fourier Coefficient Relative Magnitude (dB) - Defined In Equation 32 - For Case 3c Defined In Section 4 C.
);

Supp Figure 12 Sorted Coefficients Case 3c

@usgov.national_institute_of_standard_data_for_on_grid_compre_31ae5c2c.supp_figure_12_sorted_coefficients_case_3c

136 kB
4,699 rows
6 columns

CREATE TABLE supp_figure_12_sorted_coefficients_case_3c (
  "number_of_wigner_d_coefficients_kept_no_relevant_units" VARCHAR  -- Number Of Wigner D Coefficients Kept (no Relevant Units).,
  "normalized_error_of_kept_wigner_d_coefficeints_db_defi_02af1c1a" VARCHAR  -- Normalized Error Of Kept Wigner D Coefficeints (dB) - Defined In Equation 33 - For Case 3c Defined In Section 4 C.,
  "number_of_fourier_coefficients_kept_no_relevant_units" BIGINT  -- Number Of Fourier Coefficients Kept (no Relevant Units).,
  "normalized_error_of_kept_fourier_coefficeints_db_defin_5f10a51a" DOUBLE  -- Normalized Error Of Kept Fourier Coefficeints (dB) - Defined In Equation 33 - For Case 3c Defined In Section 4 C.,
  "number_of_fourier_coefficients_kept_no_relevant_units_1" BIGINT  -- Number Of Fourier Coefficients Kept (no Relevant Units)..1,
  "normalized_error_of_kept_fourier_coefficeints_transfor_efc3f151" DOUBLE  -- Normalized Error Of Kept Fourier Coefficeints Transformed Back To Wigner D Basis (dB) - Defined In Equation 33 - For Case 3c Defined In Section 4 C.
);