This paper presents reconstruction of transient acoustic radiation from impulsively accelerated objects using the HELS method [Wu, J. Acoust. Soc. Am. 107, 2511–2522 (2000)]. The radiated acoustic pressure is expanded in terms of the spherical wave functions and spherical harmonics in the frequency domain. The coefficients associated with these expansion functions are determined by matching the assumed solution to the measured acoustic pressures. The errors incurred in this process are minimized by the least squares. Once the frequency-domain solution is obtained, the transient acoustic pressure signal is reconstructed by taking an inverse Fourier transformation via the reside theorem. The objects considered include an explosively expanding sphere, impulsively accelerated rigid sphere, and impulsively accelerated baffled sphere. The acoustic pressure signals thus obtained are compared with the analytic solutions. It is shown that this methodology can be extended to a nonspherical object subject to an arbitrarily time-dependent excitation. The resulting transient acoustic pressure can be reconstructed by a convolution integral of the impulse response function to the time history of the measured acoustic pressure signals. [Work supported by NSF.]