It is challenging to develop a physics-based model for propagation through atmospheric turbulence. A number of models are currently available but are typically not based on experimental results. A fresh approach might be to construct some type of "black box" filter function for producing typical distorted sonic boom waveforms on the ground. The input to the filter could be arbitrary, non-distorted sonic boom waveforms above the turbulence. As an initial model, a single input-output system was assumed. Ground-recorded waveforms were used as outputs of the system. The transfer function between the two signals was estimated using Welch's average periodogram method. Data obtained from the 2004 Shaped Sonic Boom Experiment (SSBE) was analyzed and corresponding transfer functions were obtained. With such transfer functions established, FIR filters were determined and convolved with an appropriate input waveform. Such FIR filters allow for the production of "typical" atmospherically distorted waveforms given arbitrary input waveforms.