This chapter presents the aperiodic system resonance induced by a frequency-modulated signal. We introduce the theoretical framework of the piecewise re-scaling method and the real-time re-scaling method to achieve aperiodic system resonance under a linear or nonlinear frequency-modulated signal. The improvement of aperiodic system resonance by vibrational resonance, i.e., the effect of an auxiliary fast-varying signal in the excitation, is also clearly demonstrated.