This paper introduces a computational approach to identify performance constraints in the time-domain, offering a way to design systems in pulse operation. This work presents a comprehensive application of convex optimization to determine fundamental bounds on time-domain waveforms. The approach is applied to arbitrarily polarized multiport antennas and arrays, demonstrating their capability in maximizing peak radiation intensity in a specified direction and time under energy constraints. This methodology allows us to consider matching, which is crucial in such applications. To highlight the generality of the approach, receiving systems are also studied on an example of maximizing the local field for antiferromagnetic memory switching. Thanks to its efficacy, this work enables joint optimization of excitation and system parameters.