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According to the equivalence principle, the aperture near-field can be expressed as the convolution of the aperture field and the spatial network response function. Therefore the aperture near-field angular spectrum can be expressed as the product of the angular-domain spectrum of the aperture field and the angular-domain spectrum of the spatial network response function. The spatial network function acts as an angular spectrum filter. Based on the aperture field convolution method, the near-field radiation of several electrically large apertures has been computed and compared in the spatial and angular domains, including a circular aperture, a square aperture and a well-designed serrated edge aperture. The following facts have been demonstrated by the numerical results: The serrated edge aperture has the most uniform near-field amplitude and phase distribution, both in the transverse plane and in the central axis. The plane-wave spectrum components received by a certain observation plane are related to its position, size and shape. The direct wave and edge diffraction waves can be observed qualitatively and quantitatively in the angular domain. The edge diffraction waves cannot be distinguished when the transverse size of the observation plane is less than a certain value. Finally, based on general rules of compact antenna test range design, the angular-domain analysis applications for the evaluation of the aperture shape design and the diagnosis of the aperture deformation are presented. All the three aperture diameters are limited to 150 wavelengths in free space. Inverse Fourier transform with a Hamming window has been adopted for the spatial-angular transform.