The time-modulated array is a simple array architecture in which each antenna is connected to an RF switch that serves as a modulator. The phase shift is achieved by digitally controlling the relative delay between the periodic modulating sequences of the antennas. The practical use of this architecture is limited by two factors. First, the switching frequency is high, as it must be a multiple of the sampling frequency. Second, the discrete modulating sequence introduces undesired harmonic replicas of the signal with non-negligible power. In this paper, aliasing is exploited to simultaneously reduce sideband radiation and switching frequency. To facilitate coherent combining of aliased signal blocks, the transmit signal has a repeated block structure in the frequency domain. As a result, a factor $A$ reduction in switching frequency is achieved at the cost of a factor $A$ reduction in communication capacity. Doubling $A$ reduces sideband radiation by around 2.9 dB.