This report presents a computational technique for the rapid, efficient calculation of fields from transient acoustic sources in linear, isotropic media. The source velocity is separable in space and time. The method uses a spatial impulse response method based on linear systems concepts to express the output in terms of the Green's function of propagation equation and the boundary conditions. The output is expressed as the inverse spatial transform of the product of the transform of the spatial excitation and a time- varying spatial filter that represents propagation. The calculation technique has been implemented in MATLAB and sample cases are presented for the circular and square piston, as well as a Gaussian- and Bessel-weighted spatial excitation. Code for the MATLAB implementation is provided. Acoustic propagation, Transient waves, Transfer function, Linear systems theory.