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In this paper we present a simple and effective method, based on appropriatesuperpositions of Bessel-Gauss beams, which in the Fresnel regime is able todescribe in analytic form the 3D evolution of important waves as Bessel beams,plane waves, gaussian beams, Bessel-Gauss beams, when truncated by finiteapertures. One of the byproducts of our mathematical method is that one can getin few seconds, or minutes, high-precision results which normally require quitelong times of numerical simulation. The method works in Electromagnetism(Optics, Microwaves,...), as well as in Acoustics.  OCIS codes: (999.9999) Non-diffracting waves; (260.1960) Diffraction theory;(070.7545) Wave propagation; (070.0070) Fourier optics and signal processing;(200.0200) Optics in computing; (050.1120) Apertures; (070.1060)Acousto-optical signal processing; (280.0280) Remote sensing and sensors;(050.1755) Computational electromagnetic methods.

A simple and effective method for the analytic description of important optical beams, when truncated by finite apertures