Secondary radiation emission of laser-induced filaments is revisited from a perspective of transient antenna radiation. Solutions for transient-antenna radiation fields are shown to provide an accurate description of the spectral and polarization properties, radiation patterns, and the angular dispersion of terahertz and microwave radiation emitted by laser filaments. Time-domain pulsed-antenna analysis offers a physically clear explanation for the bandwidth of this radiation, relating the low-frequency cutoff in its spectrum to the filament length, thus explaining efficient microwave generation in laser filamentation experiments.