Data For "On-grid Compressive Sampling For Spherical Field Measurements In Acoustics" In The Journal Of The Acoustical Society Of America.
Department of Commerce
@usgov.doc_gov_data_for_on_grid_compressive_sampling_for_sphe_80b48660
Department of Commerce
@usgov.doc_gov_data_for_on_grid_compressive_sampling_for_sphe_80b48660
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: Department of Commerce
Last updated: 2025-09-30T05:14:20.373600
Tags: acoustic-fields, antenna-characterization, compressive-sampling, compressive-sensing, far-field-pattern, near-field-pattern, sparse-signal-processing, spherical-harmonics, wigner-d-functions
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.
);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.
);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."
);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."
);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."
);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.
);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."
);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."
);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."
);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.
);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.
);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.
);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.
);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.
);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.
);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.
);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.
);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.
);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.
);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.
);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.
);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."
);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.
);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.
);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.
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