Dynamical Energy Analysis (DEA) was introduced in 2009 as a novel method for predicting high-frequency acoustic and vibrational energy distributions. In this work we detail how DEA can be reformulated in the time-domain by means of a convolution integral operator and apply the Convolution Quadrature (CQ) method to discretise in time. The CQ method provides a link between the frequency domain and fully time-dependent solutions by means of the Z-transform. The space and momentum variables may be approximated using the same approaches that have previously been implemented in frequency domain DEA. The final result is a fully time-dependent DEA method that can track the propagation of high-frequency transient signals through phase-space
