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.