This paper deals with the fourth in a sequence of canonical problems aimed toward an understanding of the time domain (TD) behavior of wideband-excited sequentially pulsed planar periodic finite arrays of dipoles, which play an important role in a variety of practical applications. The present investigation of sequentially pulsed semi-infinite planar dipole arrays extends our previous studies of sequentially pulsed infinite and semi-infinite line dipole arrays and of infinite planar dipole arrays. The discrete element-by-element radiations are converted collectively to radiations from a series of Floquet wave (FW)-modulated truncated smooth equivalent aperture distributions, and to corresponding FW-modulated edge diffraction. After a summary of necessary results from the earlier studies, emphasis is placed on the new truncation-induced TD results and interpretations, which are extracted via phenomenology-matched high-frequency asymptotics from rigorous frequency and time domain formulations parameterized in terms of the dispersive FW instantaneous frequencies and wave numbers. As in our previous studies, the outcome is a numerically efficient, physically incisive algorithm whose accuracy is verified preliminarily by application to a pulsed planar strip array of dipoles.