Flexible frequency controls are crucial in many photonic and electronic applications, ranging from communications systems, spectroscopy, and metrology to quantum information processing. However, the state-of-the-art solutions based on nonlinear bulk media, electro-optic effect, and nonlinear metasurfaces incur very limited spectral controllability, and merely a couple of harmonic orders can be independently manipulated. Here, we theoretically propose and experimentally demonstrate synthetic moving-envelope metasurface antennas capable of simultaneously generating arbitrary harmonic orders and independently manipulating their wave properties in a software-defined manner. As proof-of-principle examples, we demonstrate unidirectional frequency transition, frequency comb generation, arbitrary harmonic orders independent control, and their applications in frequency-division multiplexing communications. All these complicated functionalities are achieved by the 1-bit spatiotemporally ON-OFF switching of meta-atoms of the waveguide-integrated metasurface antenna. Our proposed synthetic metasurface antenna solution greatly expands the frontiers of wave engineering and information manipulation, showing promising potential in wireless communications, spectroscopy, metrology, and quantum science.