The numerically implemented angular spectrum approach (ASA) is investigated in terms of the characteristics of the ASA as a function of angular range over which the angular spectrally decomposed plane waves are superimposed to construct an acoustic field radiated by a source. The investigation is based on the evaluation of the 2‐D fields radiated by striplike planar sources and 1‐D linear phased arrays with different aperture sizes and on the comparison with those obtained by using the analytical solution derived with the point spread function method. The convergence and the spatial aliasing of the ASA’s results are systematically dealt with. A region well converging to the analytical solution as the angular range increases is found to exist before the aliasing comes up. Analytical formulas to determine the boundaries of this region are given. Based on the instantaneous frequency concept, an analytical expression for optimal selection of the angular range used is derived. Hence the sampling frequency can be chosen to be optimal and adaptive to the discretization size of the source plane without worrying that the number of the samples for the discretization size should be chosen to be a power of two that the fast Fourier transform (FFT) usually needs. An excellent agreement of the ASA’s results with the analytical solution is demonstrated when using the optimal selection of the angular range for the specified parameters. The analysis made in this paper can be extended to the case of 3‐D fields.