Figure 1

The discrete shocklet transform is generated through cross-correlation of pieces of shocks. this figure displays effects of the action of group elements \(r_{i} \in R_{4}\) on a base “shock-like” kernel \(\mathcal{K}\). The kernel \(\mathcal{K}\) captures the dynamics of a constant lower level of intensity before an abrupt increase to a relatively high intensity which decays over a duration of \(W/2\) units of time. By applying elements of \(R_{4}\), we can effect a time reversal (\(r_{1}\)) and abrupt cessation of intensity followed by asymptotic convergence to the prior level of intensity (\(r_{2}\)), as well as the combination of these effects (\(r _{3} = r_{1} \cdot r_{2}\))